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

The above relation shows that $B$ is similar to $C$ .Thus, the original statement is verified.

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 4

Eigenvectors and Linear Transformations

Vectors

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Use $A=\left[\begin{array}…

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whereas to prove that if the Matrix B A similar to matrix a matrix see a similar to matrix A than be a similar to seat well, because A is similar to be and is similar to see, this means that there exist in vertebral matrices, P and cue such that p in verse. P B p is equal to a and que in verse. See Q equals a. Then it follows that since both of these air equal to a P in verse, BP is equal to queue in verse. Si que so now let multiply by Q and right multiplied by Q In verse, we obtain que p in verse be p que inverse is equal to see since acute hymns Cuban versus the Identity. So it follows that C is equal to Q p Inverse B P Q. In verse, which we notice is the same as mhm p que in verse in verse be p que inverse And here, um, adding the parentheses for emphasis. So we have that the convertible matrix P Q. Inverse is such that Cuco inverse inverse times B times P Q. In verse equals C, and therefore we have. That deed is similar to see

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