Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

Verify that det $A B=(\operatorname{det} A)(\operatorname{det} B)$ for the matrices in Exercises37 and $38 .$ (Do not use Theorem $6 . )$$$A=\left[\begin{array}{ll}{3} & {0} \\ {6} & {1}\end{array}\right], B=\left[\begin{array}{ll}{2} & {0} \\ {5} & {4}\end{array}\right]$$

see the verification

Algebra

Chapter 3

Determinants

Section 2

Properties of Determinants

Introduction to Matrices

Oregon State University

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:59

Verify that det $A B=(\ope…

01:24

Refer to matrices $A$ and …

00:21

01:18

01:23

00:24

03:56

Use matrix multiplication,…

00:28

Assume that $A$ and $B$ be…

01:35

The matrices $A, B, C,$ an…

were given a pair of square matrices and were asked to verify that the determinant of the product of these matrices is equal to the product of the determined determinants of these matrices. So we have the Matrix A is given by 3061 and the Matrix B is given by 2054 So, on the one hand we have the determinant of A is equal to three minus zero is three. The determinant of B is equal to eight and so it follows that the determinant of a times the determinant of B is equal to 24. And on the other hand we have that the matrix A B well, this is 3061 times the matrix 2054 and this is equal to six plus 06 zero plus 00 12 plus five is 17 and zero plus four is four. So we get this square matrix and determinant of a B is therefore equal to 24. Therefore, the determinant of a B is equal to the determinant of a times the determinant of B. Just as the're, um six says

View More Answers From This Book

Find Another Textbook

Numerade Educator

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

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

Refer to matrices $A$ and $B$ at the right. Identify each matrix element.

Use matrix multiplication, equality of matrices, and the arbitrary matrix gi…

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

The matrices $A, B, C,$ and $D$ are defined as follows.$$\begin{aligned}…

01:07

Use Exercise 27 to show that if $\mathcal{A}$ and $\mathcal{B}$ are bases fo…

07:40

In Exercises 11–16, compute the adjugate of the given matrix, and then use T…

09:22

In Exercises 31–36, respond as comprehensively as possible, and justify your…

01:33

In Exercises 24–26, use determinants to decide if the set of vectors is line…

02:07

In Exercises 21 and 22, mark each statement True or False. Justify each answ…

02:54

In Exercises 11 and $12,$ find the dimension of the subspace spanned by the …

04:10

In Exercises $3-6,$ find an explicit description of Nul $A$ by listing vecto…

02:44

Let $T : \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$ be a linear transformati…

01:41

Is $\lambda=2$ an eigenvalue of $\left[\begin{array}{ll}{3} & {2} \\ {3}…

04:17

Exercises 31 and 32 concern finite-dimensional vector spaces $V$ and $W$ and…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.