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Verify the statements in Exercises $19-24 .$ The matrices are square.If $A$ is diagonalizable and $B$ is similar to $A,$ then $B$ is also diagonalizable.

Therefore, the matrix $B$ is diagonalizable.Therefore, the given statement is TRUE.

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 4

Eigenvectors and Linear Transformations

Vectors

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Okay, so for problem 22 were first given Matrix K, which is diagnosed Technol Izabal. So that means by definition we can have a have any murderball metrics say ass times as he first time says is De were where these are diving a matrix. Excuse me. Now also, by the definition off similarity then were given that be similar to a So we also have, um t inverse times. Hey, times t she's bi. Of course, T has to be a murderer matrix. Now we first soft a by multiplying I'm on applying t from the left hand side of right hand side so that mrs, uh, sorry. Second question. We must have a which is tee times be I'm stealing verse. Now we put the D. C. Based compression into our first question. No, we have asked members times t hey, t inverse times asked. Okay, Now here. Uh, yeah, I I missed the Dagenham matrix D on the right hand side. Now here, uh, let's take you to be a scene first times t so that, um our yeah, so our you immerse will be t t inverse times has. Okay, So since these two matrices are all in murderball, so you has to be in veritable so we can rewrite our expression here. D to be you times B times Ewing burst. So we've shown that be, by definition, bees.

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