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In Exercises 31–36, mention an appropriate theorem in your explanation.Let $A$ and $P$ be square matrices, with $P$ invertible. Show that $\operatorname{det}\left(P A P^{-1}\right)=\operatorname{det} A$

see the proof

Algebra

Chapter 3

Determinants

Section 2

Properties of Determinants

Introduction to Matrices

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

01:10

In Exercises 31–36, mentio…

01:26

01:44

Suppose $P$ is invertible …

03:26

Show that $A=P D P^{-1},$ …

03:35

02:47

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Show that $A^{2}=P D^{2} P…

03:28

02:05

If $A$ and $S$ are $n \tim…

02:51

If $A$ is an invertible $n…

okay. In this question, we want to show that determines right here is equal to determine off, eh? So how do we do this? You first separate out the products. Then it will be determines off a as a determinant four p invest. So what we do is we arranged. We rearrange. Hey, turn it off. He even this turn this all day. So pushing in the two peas? Yeah, he pilot, he in this. How's my determinant? Okay, now, Pete Pete in verse is the identity matrix Identity matrix has, like, determinants off, eh? Now, determinants off the identity matrix is just simply one. So therefore, this is just a terminus, okay?

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In mathematics, the absolute value or modulus |x| of a real number x is its …

In Exercises 31–36, mention an appropriate theorem in your explanation.F…

In Exercises 31–36, mention an appropriate theorem in your explanation.S…

Suppose $P$ is invertible and $A=P B P^{-1} .$ Solve for $B$ in terms of $A …

Show that $A=P D P^{-1},$ where $P$ is a matrix whose columns are the eigenv…

Show that $A^{2}=P D^{2} P^{-1},$ where $P$ is a matrix whose columns are th…

If $A$ and $S$ are $n \times n$ matrices with $S$ invertible, show that $\op…

If $A$ is an invertible $n \times n$ matrix, prove property $\mathrm{P} 9:$<…

01:45

Determine the dimensions of Nul $A$ and $\mathrm{Col} A$ for the matrices sh…

02:46

Find the volume of the parallelepiped with one vertex at the origin and adja…

01:33

Find the determinants in Exercises $15-20,$ where$$\left|\begin{arra…

06:43

In Exercises 23 and $24,$ mark each statement True or False. Justify each an…

04:47

01:59

Verify that det $A B=(\operatorname{det} A)(\operatorname{det} B)$ for the m…

00:39

Each equation in Exercises $1-4$ illustrates a property of determinants. Sta…

03:12

$\mathcal{B}$ and $\mathcal{C}$ are bases for a vector space $V$ Mark each s…

02:25

$[\mathbf{M}]$ With $A$ and $B$ as in Exercise $41,$ select a column $\mathb…

02:16

Let $\mathcal{A}=\left\{\mathbf{a}_{1}, \mathbf{a}_{2}, \mathbf{a}_{3}\right…

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