4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

Concept explainers

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Question

Chapter 8.2, Problem 49E

(a).

To determine

To find $AB$ , where $A=[−4−1212]$ and $B=[−65]$ .

(a).

Expert Solution

Answer to Problem 49E

$AB=[1948]$

Explanation of Solution

Given:

Consider $A=[−4−1212]$ and $B=[−65]$ .

Concept used:

If $A=[aij]$ is an $m×n$ matrix and $B=[bij]$ is an $n×p$ matrix, then the product $AB$ is an $m×p$ matrix given by $AB=[cij]$ , where $cij=ai1b1j+ai2b2j+ai3b3j+⋯+ainbnj$ .

Calculation:

Here, Since A is a $2×2$ and B is a $2×1$ matrix, therefore, there product will be of dimension $2×1$ and hence it will be possible.

$AB=[−4−1212][−65]=[−6×(−4)+5×(−1)−6×2+5×12]=[24−5−12+60]=[1948]$

(b).

To determine

To find $BA$ , where $A=[−4−1212]$ and $B=[−65]$ .

(b).

Expert Solution

Answer to Problem 49E

$BA=$ Not possible

Explanation of Solution

Given:

Consider $A=[−4−1212]$ and $B=[−65]$ .

Concept used:

If $A=[aij]$ is an $m×n$ matrix and $B=[bij]$ is an $n×p$ matrix, then the product $AB$ is an $m×p$ matrix given by $AB=[cij]$ , where $cij=ai1b1j+ai2b2j+ai3b3j+⋯+ainbnj$ .

Calculation:

Since B is a $2×1$ and A is a $2×2$ matrix, therefore, there the product $BA$ will not be possible according to the definition of the matrix multiplication which states that number of columns in matrix B should be equal to number of rows in matrix A .

(c).

To determine

To find $A2$ , where $A=[−4−1212]$ .

(c).

Expert Solution

Answer to Problem 49E

$A2=[14−816142]$

Explanation of Solution

Given:

Consider $A=[−4−1212]$ .

Concept used:

If $A=[aij]$ is an $m×n$ matrix and $B=[bij]$ is an $n×p$ matrix, then the product $AB$ is an $m×p$ matrix given by $AB=[cij]$ , where $cij=ai1b1j+ai2b2j+ai3b3j+⋯+ainbnj$ .

Calculation:

Here, A is a square matrix of dimension $2×2$ , therefore, $A2$ will be possible.

$A2=[−4−1212][−4−1212]=[−4×(−4)+2×(−1)−1×(−4)+12×(−1)−4×2+2×12−1×2+12×12]=[16−24−12−8+24−2+144]=[14−816142]$

Chapter 8.2, Problem 48E

Chapter 8.2, Problem 50E

Chapter 8 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - 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To find A B , where A = [ − 4 − 1 2 12 ] and B = [ − 6 5 ] .

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Answer to Problem 49E

Explanation of Solution

Answer to Problem 49E

Explanation of Solution

Answer to Problem 49E

Explanation of Solution

Chapter 8 Solutions