suppose-q-is-any-matrix-such-that-mathbfv_mathcalcqmathbfv_mathcalb-for-each-mathbfv-in-v-set-mathbf

Question

Suppose $Q$ is any matrix such that
$[\mathbf{v}]_{\mathcal{C}}=Q[\mathbf{v}]_{\mathcal{B}}$ for each $\mathbf{v}$ in $V$
Set $\mathbf{v}=\mathbf{b}_{1}$ in $(9) .$ Then $(9)$ shows that $\left[\mathbf{b}_{1}\right] c$ is the first column of $Q$ because (a) ______. Similarly, for $k=2, \ldots, n,$ the $k$th column of $Q$ is (b) ______ because (c) ______. This shows that the matrix $_{c \leftarrow \mathcal{B}}$ defined by $(5)$ in Theorem 15 is the only matrix that satisfies condition $(4)$ .

Thomas Emment · Accepted Answer

gate with make sure to keep is equal to B Times eight on We want to find the first row. First column element of Q on the second row. Second column Element off key. So to do this, remember Mood Image publication. It&#x27;s the Rose. The first column against Sorry Rose, the first major COMSEC matrix so fast against first G. A job against a C E here. G a to us hate C plus he I This would be equal to Q and one on bank UTC. Well, that second wrote against Second Column said JK elegant B d F. Said have JB um plus, uh, DK don&#x27;t keep come the drift king and finally f out on this is a key t t.

Robert Daugherty · Answer

Section three to Problem number 42. They give us two square four by four major cities determinant of A It&#x27;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.

Thomas Emment · Answer

Okay, we&#x27;ve been given this matrix a on. We want to prove that the identity touched by a single toe and eight times identity is equal to a So what&#x27;s the identity, Clark? The honesty for a two by two matrix is 1001 Where you can think of this matrix is almost the wonder if, like the two dimensional matrix you know, two equally Teoh. Yeah, You configure the one off the to mention round where anything times, right, This is always going to be itself. It&#x27;s got same properties as one is what we&#x27;re trying to set so that we can prove this hit. So when we do major modification, you take the rows of the first Matrix against the columns off the 2nd 1 So he will have 10 against 35130 lots of five. We just We left the three equally guessing with 1st 2nd column one a lot of that 20 lots. That nine. Now we move on to our second road and I&#x27;ll go the second column first. Remember Eyes Our first major accepting second row second column zero loss that to one on that night on Finally, we got were onto art. Second row, First column say second or the first matrix here. One first column of that second matrix 350 Is that 31? More than five. Where does Aziz? I think you&#x27;d see guys equal to a Okay. Now are a czar. First Matrix and our eyes. Our second tricks. So we taking the rose off the A matrix. So you&#x27;ve got three to hear first against 10 So one of the 30 lots. That too. Well, after this three equally stick with the first report when we come to our second column now is hear lots about 31 law. That, too. And now in our second round. First, call him one more. That 50 loss about nine. And then second row, Second column zero. It&#x27;s that 51 law that nine on. I think you can see that both of these are equal to a

Robert Daugherty · Answer

Section 36 Problem 39. So we&#x27;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&#x27;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

Robert Daugherty · Answer

section 3.2. We&#x27;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

Problem

$[\mathbf{M}]$ Let $\mathcal{B}=\left\{\mathbf{x}…

Problem 16 Easy Difficulty

Answer

A. $\left[\mathbf{b}_{1}\right]_{c}=Q \mathbf{e}_{1}$
B. $\left[\mathbf{b}_{k}\right]_{c}$
C. $Q \mathbf{e}_{k}$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Kristen K.

Vectors Intro

Vector Basics - Example 1

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A. $\left[\mathbf{b}_{1}\right]_{c}=Q \mathbf{e}_{1}$B. $\left[\mathbf{b}_{k}\right]_{c}$C. $Q \mathbf{e}_{k}$

Linear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Kristen K.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Kristen K.

A. $\left[\mathbf{b}_{1}\right]_{c}=Q \mathbf{e}_{1}$
B. $\left[\mathbf{b}_{k}\right]_{c}$
C. $Q \mathbf{e}_{k}$

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications