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Construct thc matrix(aij)x} uhcre=tor!_ 1,2and aij WtorEvaluate _and 3A whcn 4 =3)B= (5...

Question

Construct thc matrix(aij)x} uhcre=tor!_ 1,2and aij WtorEvaluate _and 3A whcn 4 =3)B= (5

Construct thc matrix (aij)x} uhcre= tor!_ 1,2 and aij Wtor Evaluate _ and 3A whcn 4 = 3) B= (5



Answers

Let $A$ and $B$ be $4 \times 4$ matrices such that $\operatorname{det}(A)=5$ and $\operatorname{det}(B)=3 .$ Compute the determinant of the given matrix. $$(4 B)^{3}$$

Section 36 Problem 39. So we're giving two matrices and be there four by four of the terminal dais. Five determinative is three and were asked to find that a term in it of a inverse B squared to the third power. So we just use properties of determinants of the determinant of a inverse B squared. Cute. So what is the This is going to be, um, so you could think of this is the determinant of a inverse B squared. Mm. Um, times the determinant a inverse B squared times, the determinant, a inverse b squared. And the other way to think about that This is just the determinant of a inverse. He's squared three times. So what is the determinant of a inverse? So if the determinant of a is five, the determinant of a inverse is 1/5. And then if the determinant of B is three, the determinant of B squared is going to be three squared, and then all of this is cubed. So this is 9/5 cubed, which is 27 over 25. Um, sorry. Back up. Nine cubed. Not nine to the third power. Um, so nine cubed is what 7 29 over 1 25 is your final answer. So again, just properties of determinants, um, and raising them to powers and trying to make the arithmetic mistake that I almost made there at the ends of 7 29/1 25

Section three days to problem 41. They give us to four by four matrices a and B the determinative A it's five. The determinant B is three and were asked to find the determinate of the matrix five a to be So this is the determinate five a times the determinant of to be. And since this is a four by four matrix, this is going to be five to the fourth determinant of a times two to the fourth determinate be is that this answer is five to the fourth determinant of a is five to to the fourth determinate of B is three. So you multiply all of these together and you should come up with ah, 150,000 should be the determinant of this matrix five A to B.

Section three to Problem number 42. They give us two square four by four major cities determinant of A It's five determined to be is three and were asked to find the determinate of be in verse a inverse Well, you know that the determinative be inverse is just gonna be won Over the determinative be the determinant of a M verses one over the determinant of a So this is going to be 1/3 terms 1/5 or one 15 is the final answer here.

Section 3.2. We're looking at problem number 38. So in this case, they give us to four. Before Major sees a m B terminates a A and B respectively, and were asked to find the determinate of a squared be to the fifth. So the determinant a square times be to the fifth That is going to be the determinant of a squared times. The determinant be to the fifth. And, uh, if you think about this, this is determine it of a times a and the determinant of the Thames be he just repeated multiplication. So it turns out that this is the determinant of a squared the determinant of B to the fifth. The determinant of a is five. So this is five squared three to the fifth, which is 25 three to the fifth is to 43. So you multiply these together and this is 607 five. So that is the determinant of a squared B to the fifth


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