Answers
so, let's use the last column, 2,0,4, because it has a zero there, and we can use that as a cofactor to simply get a 0 as a product with the minor.
[tex]\bf \begin{bmatrix} 4&-1&\boxed{2}\\ 6&-1&\boxed{0}\\ 1&-3&\boxed{4} \end{bmatrix}\impliedby \textit{let's use the 3rd column for our cofactors}\\\\ -------------------------------\\\\ \begin{bmatrix} &&\boxed{2}\\ 6&-1&\\ 1&-3& \end{bmatrix}\implies +2 \begin{bmatrix} 6&-1\\1&-3 \end{bmatrix}\implies +2[(-18)-(-1)] \\\\\\ +2(-17)\implies -34\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{bmatrix} 4&-1&\\ &&\boxed{0}\\ 1&-3& \end{bmatrix}\implies -0 \begin{bmatrix} 4&-1\\1&-3 \end{bmatrix}\implies -0[(-12)-(-1)]\implies 0\\\\ -------------------------------\\\\ \begin{bmatrix} 4&-1&\\ 6&-1&\\ &&\boxed{4} \end{bmatrix}\implies +4 \begin{bmatrix} 4&-1\\6&-1 \end{bmatrix}\implies +4[(-4)-(-6)] \\\\\\ +4[2]\implies 8\\\\ -------------------------------\\\\[/tex]
so our determinant comes down to the sum of those three products... so -34 -0 + 8.
and surely you know how much that is.
The question is about finding the value of a determinant for matrices, a fundamental concept in Mathematics, especially linear algebra. For 2 × 2 matrices, the determinant calculation is straightforward and essential for various applications.
Explanation:The subject of this question is clearly Mathematics, specifically it pertains to linear algebra and the concept of determinants. The task involves finding the value of a determinant for a given matrix. For a 2 × 2 matrix, the determinant is found using a simple formula: if the matrix is given by
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
then the determinant is calculated as \(ad - bc\). Additionally, the determinant provides important information about the matrix, such as whether the matrix is invertible and the product of its eigenvalues.
To understand determinants for larger matrices, a recursive approach is often used, breaking down the determinant into smaller matrices until 2 × 2 matrices are reached, where the simple formula can be applied. Also of note is that the determinant of the product of two matrices is equal to the product of their determinants (det(AB) = det(A)det(B)).
This fundamental concept is crucial for many applications in mathematics, including solving systems of linear equations, finding eigenvalues, and understanding linear transformations.
Related Questions
If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?
Answers
The commutative property allows you to rearrange the factors of a multiplication problem.
Explanation:The property that allows you to rearrange the factors of a multiplication problem is the commutative property. This property states that the order of the factors can be changed without changing the product. In this case, if cba represents three numbers multiplied together, you can rearrange the factors to read abc because multiplying in any order will give you the same product.
For example, if c = 2, b = 3, and a = 4, then cba = 2 * 3 * 4 = 24. Rearranging the factors to abc gives abc = 4 * 3 * 2 = 24, which is the same product.
let A and B be nxn matrices such that AB is singular prove that either A or Bis singular
Answers
Because [tex]\mathbf{AB}[/tex] is singular, we have
[tex]\det(\mathbf{AB})=0[/tex]
from which it follows that either [tex]\det\mathbf A=0[/tex] or [tex]\det\mathbf B=0[/tex].
How can you use place value and period names to read and write 324,904 in word form.
Answers
three hundred twenty four thousand, nine hundred four.
no ands were in between the numbers because there are no decimals.
hope this helped, xx
3. Solve z2 – 15z + 56 = 0 using the zero product property. A. z = 8, 7 B. z = –5, –2 C. z = 8, –4 D. z = –4, 7
Answers
z² - 15z + 56 = 0
The expression will have a and b values such as a = - 7 and b = -8.
z² - 15z + 56 = 0
(z -7) (z-8) = 0
solving for the first value of z, we have it:
z - 7 = 0
z = 7
Solving for the second value of z, we have it:
z - 8 = 0
z = 8
Therefore, the answer to this problem is the letter "A" which is 7 and 8.
Hello, I'm working on a project and I've been stumped.
How would I find the central ark of a ferris wheel? I'm using the London Eye ferris wheel for my project, and so far I know it has a diameter of 120 meters and 32 cars. It has a circumference of 377m and an area of 11,310m.
How can that information help me? Please include all steps and a clear explanation, and give the answer in degrees. Thank you.
Answers
a circle has 360 degrees
the ferris wheel has 32 cars so the circle is broken up into 32 sections
the central angle would be the angle between 2 of the cars
so divide 360 by 32
360/32 = 11.25 degrees
Compare the value of the
4 in 40 and 400
Answers
For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is
Answers
P(X≤−1.9)=0.0287165598160018P(X≤−1.9)=0.0287165598160018
P(X≥1.7)=0.044565462758543P(X≥1.7)=0.044565462758543
P(−1.95996398454005≤X≤1.95996398454005)=0.95
Answer:
92.67% probability of obtaining a z value between -1.9 to 1.7.
Step-by-step explanation:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is
This probability is the pvalue of z = 1.7 subtracted by the pvalue of z = -1.9.
z = 1.7 has a pvalue of 0.9554.
z = -1.9 has a pvalue of 0.0287.
So there is a 0.9554-0.0287 = 0.9267 = 92.67% probability of obtaining a z value between -1.9 to 1.7.
There is a value of a such that subtracting a-4 from 4a+16 gives an answer of -25. What is that value of a?
Answers
4a+16 - (a-4) = 3a + 20 = 25 => 3a = 5 => a = 5/3
Suppose there is a test for esophageal cancer that is 95% accurate both on those that do and those that do not have esophageal cancer. if 0.7 percent of the population has esophageal cancer, compute the probability that a person has this cancer, given that his or her test results indicates so.
Answers
Probability = (0.007)(0.95) = 0.00665 or 0.665%
So instead of 0.7%, the probability will decreased to 0.665% because of the accuracy.
An employer interviews 10 people for 6 technical support positions in a company, and 5 of the 10 people are women. If all 10 are qualified, in how many ways can the employer fill the technical support positions if exactly 3 are women?
Answers
where M1 is Man 1, W1 woman 1 and so on...
The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], gives the total numbers of ways of creating groups of r out of n.
r! means 1*2*3*...(r-1)*r.
The technical support group is going to have exactly 3 women, which will be chosen from 5 women, and 3 men which will be chosen from 5 men.
Each of the selections can be done in C(5, 3) many ways, and since the any selection of the men and women can be combined, in total there are:
C(5,3) *C(5, 3) many ways of creating the technical support group.
[tex]C(5,3) = \frac{5!}{3!2!}= \frac{5*4*3*2*1}{3*2*1*2*1}=10 [/tex]
10*10=100 many ways of forming the group.
Answer: 100
To put up several tents for a camping trip, you need several pieces of rope each 6 2/3 feet long. If you have a rope that is 43 feet, how many pieces can you cut for the tents?
Answers
Will someone please answer this question?
Answers
surface area = 5ab +5bh
a = 4
b=7
h=18
5*4*7 = 140
5*7*18 = 630
630+140 = 770 square meters
Estimate then find the product 7×7956
Answers
Final answer:
To estimate the product of 7 and 7956, round 7956 to 8000 and then multiply by 7 to get 56,000. The exact product, calculated using the multiplication algorithm, is 55,692.
Explanation:
To estimate the product of 7×7956, we can round 7956 to the nearest thousand which gives us 8000. Then, we multiply 7×8000 to get an estimated product of 56,000. To find the exact product, we multiply 7 by 7956 to get 55,692.
When calculating such a product, we use the multiplication algorithm where we multiply each digit of the second number by the first number and then add up the resulting values.
Here's how you would perform the multiplication step by step:
7×7 = 49, add the carried over 6 to get 55, write down 5 and carry over the 5.
After placing the digits in their correct positions, we get the final answer: 55,692. Therefore, the exact product of 7×7956 is 55,692.
If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45
Answers
is
gcd(m*m*n*n, m*n*n*n) =m*n*n=[tex]m n^{2} [/tex]
what we did, was to see how many m's and how many n's, each expression have, and then pick the smallest of each letter (factor).
the reason is that the common factor, must have enough m's and n's to divide the m's and n's of both expressions
so
[tex]45=m n^{2} [/tex]
also
[tex]45=5*9=5*3^{2}[/tex]
thus, n is equal to 3
Answer: A)3
The equation of the line of best fit of a scatter plot is y = −4x − 6. What is the slope of the equation?
−6
−4
4
6
Answers
y=mx+b, where m=slope and b=y-intecept
So if y=-4x-6 the slope is -4.
the equation is written in slope intercept form ( y = mx +b ) where b is the y intercept
therefore the y intercept is -6
Susie is paying $502.33 every month for her $150,000 mortgage payment. If this is a 4.5% 30 year mortgage, how much interest will she pay over the 30 years of payments?
Answers
502.33(12)30-150000=total interest paid
i=502.33(12)30-150000
i=$30838.80
Answer:
$30838.80
:3 simply it pls
Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds that each picket fence slat is two feet wide. If Curt does not want any spaces between each slat, use estimation to determine how many slats of fencing he should buy.
Answers
P = 45.45 + 45.45 + 14.63 + 14.63 = 120.16 feet
One picket fence slat is 2 feet wide, so the number of fence Curt should buy is
120.16÷2 = 60.08 rounded to 61 fences
Jane is making a suit which requires 2 5/8 yards for the jacket and 1 3/4 yards for the skirt. What is the total amount of material she needs? A. 3 1/2 yards B. 3 2/3 yards C. 4 yards D. 4 3/8 yards Mark for review (Will be highlighted on the review page)
Answers
1 3/4 >>> 1 6/8 ( the 6 comes from 8/4 x 3)
The total material that jane need would be:
2 5/8 + 1 6/8
= 3 11/8
= 4 3/8
The answer is option D,
Can you help me solve this 2/3 (5 x 4) ÷ 3 + 6/7 =
Answers
this is the order you do the math
parenthesis
exponents
multiplication or division which ever is first
Addition or subtraction which ever is first
2/3 (5 x 4) ÷ 3 + 6/7
2/3 (20)÷3+6/7
40/3÷3+6/7
40/9+6/7
find common denominator
280/63+54/63
334/63 or 5.301
Look at the radian measure for every 30 degrees and 45 degrees in the Unit Circle. Explain how finding the exact measure in quadrant one can help you determine the remaining exact radian measures.
Answers
Lena bought 10 pounds of potatoes for $5.50 write the cost as cents per pound
Answers
one pound = $5.50 / 10 = $0.55
answer
it cost 55 cents per pound
Txt me quicky i need help
Answers
P(even) = 4/8
simplified is 1/2
hope this helps
For each function, use the slope formula to calculate the rate of change between the points. In your final answer, include all of your calculations.
f(x):
(a, f(a) and (b,f(b)
1.) f(x)=x - 3 (0,f(0)) and (6,f(6))
2.) f(x) = -x (-4,f(-4)) and(2,f(2))
3.) f(x)=x2 (-2,f(-2)) and (0,f(0))
4.) f(x)=x3 (-1,f(-1)) and (1,f(1))
5.) f(x)=2x (0,f(0)) and (4,f(4))
Answers
f(x) = x - 3
f(0) = 0 - 3 = -3
f(6) = 6 - 3 = 3
Slope = [tex] \frac{-3-3}{6-0} = \frac{-6}{6} =-1[/tex]
Function 2:
f(x) = -x
f(-4) = 4
f(2) = -2
Slope = [tex] \frac{4--2}{-4-2}= \frac{6}{-6}=-1 [/tex]
Function 3:
f(x) = x²
f(-2) = (-2)² = 4
f(0) = (0)² = 0
Slope = [tex] \frac{4-0}{-2-0}= \frac{4}{-2}=-2 [/tex]
Function 4:
f(x) = x³
f(-1) = (-1)³ = -1
f(1) = (1)³ = 1
Slope = [tex] \frac{-1-1}{-1-1}= \frac{-2}{-2}=1 [/tex]
Function 5:
f(x) = 2ˣ
f(0) = 2⁰ = 1
f(4) = 2⁴ = 16
Slope = [tex] \frac{1-16}{0-4}= \frac{-15}{-4}=3.75 [/tex]
If 3/2 divided by 1/4 =n, then n is between
Answers
3*4= 12
2*1= 1
n= 12/1 or 12
Hope this helps!
There are 12 more toy cars than toy trucks in a toy box. With a total of 38 toy cars and trucks.How many toy trucks are in the toy box?
Answers
i just simply do like this
38÷2
=19-12
=7
38-7
=31#
Answer:
Hui
Step-by-step explanation:
Linear regression describes the extent to which _______ predicts ________.
Answers
Linear regression describes the extent to which an independent variable predicts a dependent variable through a linear relationship.
Explanation:Linear regression describes the extent to which an independent variable (x) predicts a dependent variable (y) through a linear relationship.
For example, if we have data that shows the number of hours studied (x) and the test score (y) of students, linear regression can help us determine how well the number of hours studied predicts the test score.
The regression line is used to model the linear relationship between the independent and dependent variables in the population.
Learn more about Linear regression here:https://brainly.com/question/36829492
#SPJ12
the formula I=square root w/r gives the electric current I amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms. which set of numbers best describes the value of I for the given values of W and R? ( 42.) W=100,R=25 ( 43.)W=100,R=50
Answers
Final answer:
The value of I for the given values of W and R can be calculated using the formula I = [tex]\sqrt{(W/R)[/tex]. For W = 100 and R = 25, the value of I is 2 amperes. For W = 100 and R = 50, the value of I is approximately 1.41 amperes.
Explanation:
The formula I = [tex]\sqrt{(W/R)[/tex] gives the electric current in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms.
To determine the value of I for the given values of W and R, we can simply substitute the values into the formula. For the first set of numbers, W = 100 and R = 25:
[tex]I = \sqrt{(100/25)} = \sqrt{(4)} = 2[/tex] amperes.
For the second set of numbers, W = 100 and R = 50:
[tex]I = \sqrt{(100/50)} = \sqrt{(2) }[/tex]≈ 1.41 amperes.
Therefore, the value of I for the first set of numbers (W = 100, R = 25) is 2 amperes, and the value of I for the second set of numbers (W = 100, R = 50) is approximately 1.41 amperes.
EASY 5 POINTS REALLY NEED HELP RN!!!! Which expression finds the length of side x in this right triangle?
Answers
x² = (8.5)² + (5)²
x = √[(8.5)² + (5)²]
Answer:
Top right one
Step-by-step explanation:
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A flagpole cast a shadow 16 feet long at the same time a pole 9 feet high casts a shadow 6feet long what is the height in feet of the flagpole
Answers
X/16=9/6
X=24
box contains 15 items,4 of which are defective and 11 are good. Two items are selected. What is probability that the first is good and the second defective?
Answers
Since we have taken 1 item out the remaining total is now 14, so the probability of getting a defective item is now 4/14.
Now you multiply the probabilities together to get (11/15)(2/7)=22/105
Final answer:
The probability that the first item selected is good and the second item is defective is 22/105.
Explanation:
To find the probability that the first item selected is good and the second item is defective, we need to consider the total number of items, the number of good items, and the number of defective items.
The total number of items is 15, with 11 being good and 4 being defective. When we select the first item, there are 15 options, out of which 11 are good. Therefore, the probability of selecting a good item first is 11/15.
After selecting the first item, there are now 14 items left in the box, with 10 being good and 4 being defective. When we select the second item, there are 14 options, out of which 4 are defective. Therefore, the probability of selecting a defective item second is 4/14, which simplifies to 2/7.
To find the probability that both events occur, we multiply the probabilities: (11/15) * (2/7) = 22/105.