We found a counterexample, so the statement is false.
<h3>
Is the statement true?</h3>
Let's use the matrix:
![\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-2%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C%200%260%260%261%20%5Cend%7Barray%7D%5Cright%5D)
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
![\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%2F2%260%260%260%5C%5C0%26-1%260%260%5C%5C0%260%26-1%260%5C%5C%200%260%260%26-1%20%5Cend%7Barray%7D%5Cright%5D)
If we multiply it by 2, we get:
![\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%26-2%260%260%5C%5C0%260%26-2%260%5C%5C%200%260%260%26-2%20%5Cend%7Barray%7D%5Cright%5D)
The adjoint of that is the original matrix, actually:
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
If you want to learn more about matrices:
brainly.com/question/11989522
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8 feet x 10 = 80 feet of pipes. 80 x 12 = 960 inches of pipes.
960 inches of pipes / 18 inch piece = 53 and 6/18 = 53 and 1/3
You can get 53 pieces at 18 inches apiece with 6 inches of pipe left over.
Answer: 8:1, 16:2, 24:3,40:5
Step-by-step explanation:
Answer:
Step-by-step explanation:
4 (x + 3) = 2x + 8 <----"four times the sum of a number and three is equal to eight more than twice the number."
Second, we want to solve the equation:
4 (x + 3) = 2x + 8
4x + 12 = 2x + 8
2x + 12 = 8 <-------subtract 2x from both sides of the equation.
2x = -4 <-------subtract -12 from both sides
x = -2 <-------divide both sides by 2 which leaves a negative answer
Third, we want to check the answer by substituting the value of -2 for x in the original equation.
4 (x + 3) = 2x + 8
4 (-2 +3) = 2(-2) + 8
-8 + 12 = -4 + 8
4 = 4
4 (x + 3) = 2x + 8 <----"four times the sum of a number and three is equal to eight more than twice the number."
Second, we want to solve the equation:
4 (x + 3) = 2x + 8
4x + 12 = 2x + 8
2x + 12 = 8 <-------subtract 2x from both sides of the equation.
2x = -4 <-------subtract -12 from both sides
x = -2 <-------divide both sides by 2 which leaves a negative answer
Third, we want to check the answer by substituting the value of -2 for x in the original equation.
4 (x + 3) = 2x + 8
4 (-2 +3) = 2(-2) + 8
-8 + 12 = -4 + 8
4 = 4
