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In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorname{det} A),$ where $E$ is the elementary matrix shown and $A=\left[\begin{array}{cc}{a} & {b} \\ {c} & {d}\end{array}\right]$$$\left[\begin{array}{ll}{1} & {k} \\ {0} & {1}\end{array}\right]$$

the property $\operatorname { det } ( E A ) = ( \operatorname { det } E ) ( \operatorname { det } A )$

Algebra

Chapter 3

Determinants

Section 1

Introduction to Determinants

Introduction to Matrices

Oregon State University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

02:11

In Exercises $33-36,$ veri…

01:42

01:52

01:59

Verify that det $A B=(\ope…

00:56

Assume that $A$ and $B$ be…

02:32

Find (a) $\operatorname{de…

05:36

14:39

In Exercises $27-36,$ find…

00:45

In Exercises $1-4$a. G…

02:52

If $A=\left[\begin{array}{…

different today. We're going to solve problem number 33 here to do Tom and is given by one. Okay. Zero lot determinant off is given the uh huh. The see the so he will be equals a plus. Casey B plus Katie seat The determinant off e equals a press case into the minus B plus Katie into city 80 plus k c V minus BC Linus K. D. C. So it it's like a d minus b c. Then this is a This is it determinant off equals what return mint off equals a T minus busy So determinant off e equals determinant off into the dominant off.

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

In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorn…

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

Assume that $A$ and $B$ be $3 \times 3$ matrices with $\operatorname{det}(A)…

Find (a) $\operatorname{det}(A),$ (b) the matrix of cofactors $M_{C},(\mathr…

Find (a) $\operatorname{det}(A),$ (b) the matrix of cofactors $M_{C} (\mathr…

In Exercises $27-36,$ find (if possible) the following matrices:$$\begin…

In Exercises $1-4$a. Give the order of each matrix.b. If $A=\left[a_…

If $A=\left[\begin{array}{rrr}1 & -1 & 2 \\ 3 & 1 & 4 \\ 0 &…

02:45

Use Theorem 3 (but not Theorem 4$)$ to show that if two rows of a square mat…

02:10

Determine by inspection whether the vectors are linearly independent. Justif…

02:59

[M] Determine if $\mathbf{y}$ is in the subspace of $\mathbb{R}^{4}$ spanned…

02:53

Suppose a linear transformation $T : \mathbb{R}^{n} \rightarrow \mathbb{R}^{…

03:25

In Exercises 15 and $16,$ find $A$ such that the given set is $\operatorname…

03:02

In Exercises $5-8,$ find the coordinate vector $[\mathbf{x}]_{\mathcal{B}}$ …

02:48

Repeat Exercise 5 with $C=\left[\begin{array}{cc}{.1} & {.6} \\ {.5} &am…

02:42

Each statement in Exercises 33–38 is either true (in all cases) or false (fo…

Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\}$ be a…

03:13

In Exercises 11 and $12,$ give integers $p$ and $q$ such that Nul $A$ is a s…

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