Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 2.3, Problem 51E

a.

To determine

To find: the values of a, b, c, and d to make the statement true.

a.

Expert Solution
Check Mark

Answer to Problem 51E

  

  a=1b=0c=0d=1

Explanation of Solution

Given information: The given matrix equation is as follows:

  [24  35][acbd]=[24  35]

Calculation:

First evaluate the determinant of first matrix as follows:

  |24  35|=[(2)(5)][4(3)]              =1012              =2

This means that this matrix has inverse. Multiply the whole equation with the inverse from the left side to calculate the inverse as shown below.

  [24  35][acbd]=[24  35][24  35]1[24  35][acbd]=[24  35][24  35]1

Matrix multiplied with its inverse is identity matrix. So,

  I[acbd]=I[10  0  1][acbd]=[10  0  1][acbd]=[10  0  1]

Therefore, the values of a, b, c, and d is 1, 0, 0, and 1 respectively.

b.

To determine

To find: and explain the result if matrix containing two column is multiplied by the matrix containing a, b, c, and d.

b.

Expert Solution
Check Mark

Answer to Problem 51E

  [acbd]=[10  0  1]

Any matrix multiplied by the identity matrix is that same matrix.

Explanation of Solution

Given information: The given matrix equation is as follows:

  [24  35][acbd]=[24  35]

Calculation:

The matrix evaluated in part a. is as follows:

  [acbd]=[10  0  1]=I

Since matrix containing a, b, c, and d is identity matrix, and any matrix multiplied by the identity matrix is that same matrix.

Example: If A is any matrix with two columns, then AI=A .

Chapter 2 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.2 - Prob. 1CFUCh. 2.2 - Prob. 2CFUCh. 2.2 - Prob. 3CFUCh. 2.2 - Prob. 4CFUCh. 2.2 - Prob. 5CFUCh. 2.2 - Prob. 6CFUCh. 2.2 - Prob. 7CFUCh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.3 - Prob. 1CFUCh. 2.3 - Prob. 2CFUCh. 2.3 - Prob. 3CFUCh. 2.3 - Prob. 4CFUCh. 2.3 - Prob. 5CFUCh. 2.3 - Prob. 6CFUCh. 2.3 - Prob. 7CFUCh. 2.3 - Prob. 8CFUCh. 2.3 - Prob. 9CFUCh. 2.3 - Prob. 10CFUCh. 2.3 - Prob. 11CFUCh. 2.3 - Prob. 12CFUCh. 2.3 - Prob. 13CFUCh. 2.3 - Prob. 14CFUCh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.4A - Prob. 1GCECh. 2.4A - Prob. 2GCECh. 2.4A - Prob. 3GCECh. 2.4A - Prob. 4GCECh. 2.4A - Prob. 1MCQCh. 2.4A - Prob. 2MCQCh. 2.4A - Prob. 3MCQCh. 2.4A - Prob. 4MCQCh. 2.4A - Prob. 5MCQCh. 2.4A - Prob. 6MCQCh. 2.4A - Prob. 7MCQCh. 2.4A - Prob. 8MCQCh. 2.4A - Prob. 9MCQCh. 2.4A - Prob. 10MCQCh. 2.4 - Prob. 1CFUCh. 2.4 - Prob. 2CFUCh. 2.4 - Prob. 3CFUCh. 2.4 - Prob. 4CFUCh. 2.4 - Prob. 5CFUCh. 2.4 - Prob. 6CFUCh. 2.4 - Prob. 7CFUCh. 2.4 - Prob. 8CFUCh. 2.4 - Prob. 9CFUCh. 2.4 - Prob. 10CFUCh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.5 - Prob. 1CFUCh. 2.5 - Prob. 2CFUCh. 2.5 - Prob. 3CFUCh. 2.5 - Prob. 4CFUCh. 2.5 - Prob. 5CFUCh. 2.5 - Prob. 6CFUCh. 2.5 - Prob. 7CFUCh. 2.5 - Prob. 8CFUCh. 2.5 - Prob. 9CFUCh. 2.5 - Prob. 10CFUCh. 2.5 - Prob. 11CFUCh. 2.5 - Prob. 12CFUCh. 2.5 - Prob. 13CFUCh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5B - Prob. 1GCECh. 2.5B - Prob. 2GCECh. 2.5B - Prob. 3GCECh. 2.5B - Prob. 4GCECh. 2.5B - Prob. 5GCECh. 2.6 - Prob. 1CFUCh. 2.6 - Prob. 2CFUCh. 2.6 - Prob. 3CFUCh. 2.6 - Prob. 4CFUCh. 2.6 - Prob. 5CFUCh. 2.6 - Prob. 6CFUCh. 2.6 - Prob. 7CFUCh. 2.6 - Prob. 8CFUCh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.7 - Prob. 1CFUCh. 2.7 - Prob. 2CFUCh. 2.7 - Prob. 3CFUCh. 2.7 - Prob. 4CFUCh. 2.7 - Prob. 5CFUCh. 2.7 - Prob. 6CFUCh. 2.7 - Prob. 7CFUCh. 2.7 - Prob. 8CFUCh. 2.7 - Prob. 9ECh. 2.7 - Prob. 10ECh. 2.7 - Prob. 11ECh. 2.7 - Prob. 12ECh. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2 - Prob. 1SGACh. 2 - Prob. 2SGACh. 2 - Prob. 3SGACh. 2 - Prob. 4SGACh. 2 - Prob. 5SGACh. 2 - Prob. 6SGACh. 2 - Prob. 7SGACh. 2 - Prob. 8SGACh. 2 - Prob. 9SGACh. 2 - Prob. 10SGA

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