Nature of Mathematics (MindTap Course List)
Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Chapter 16.CR, Problem 1CR
To determine

To perform:

To perform the matrix operations for CB-3D where

A=102-1 B=2-10101
C= 2012-11 D=010-10001-1

Expert Solution & Answer
Check Mark

Answer to Problem 1CR

Solution:

4-507-12-1-24

Explanation of Solution

Approach:

Fundamental Matrix operations are equality, addition, subtraction, multiplication by a scalar and multiplication.

Equality: Two matrices [A] and [B] are said to be equal if and only if matrices are of same order and the corresponding entries are the same.

Addition: When two matrices A and B are added, the resulting matrix [C] is obtained if and only if the both matrices are of same order and the entries are found by adding the corresponding entries.

Subtraction: When matrix B is subtracted from [A], the resulting matrix [C] is obtained if and only if the both matrices are of same order and the entries are found by subtracting the entries of [B] from the corresponding entries of [A].

Multiplication by a scalar: If a matrix [A] is multiplied by the scalar (real number) x, the resulting matrix is the matrix in which each entry is multiplied by x.

Multiplication: Let [A] be an m×r matrix and [B] be an r×n matrix. The product of AB=[C] is an m×n matrix. The entry in the i th row and j th column of [A][B] is the sum of the products formed by multiplying each entry of the i th row of [A] by the corresponding entry in the j th column of B.

Check whether the number of columns of [A] is equal to the number of rows of [B]

Calculation:

Given matrix operation is CB-3D

B=2-10101 C= 2012-11 D=010-10001-1

In order to multiply two matrices, columns of first matrix should be equal to rows of the second matrix.

Check whether the number of columns of [C] is equal to the number of rows of [B].

C=3×2,B=2×3

Therefore, CB=3×3 matrix.

CB= 2012-112-10101

=2×2+0×12×-1+0×02×0+0×11×2+2×11×-1+2×01×0+2×1-1×2+1×1-1×-1+1×0-1×0+1×1

=4+0-2+00+02+2-1+00+2-2+11+00+1

=4-204-12-111

3D=3010-10001-1

=3×03×13×03×-13×03×03×03×13×-1

=030-30003-3

CB-3D=4-204-12-111-030-30003-3

=4-0-2-30-04--3-1-02-0-1-01-31--3

=4-507-12-1-24

Final statement:

The matrix operation of CB-3D=4-507-12-1-24

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Chapter 16 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 16.1 - Prob. 11PSCh. 16.1 - Prob. 12PSCh. 16.1 - Prob. 13PSCh. 16.1 - Prob. 14PSCh. 16.1 - Prob. 15PSCh. 16.1 - Prob. 16PSCh. 16.1 - Prob. 17PSCh. 16.1 - Prob. 18PSCh. 16.1 - Prob. 19PSCh. 16.1 - Prob. 20PSCh. 16.1 - Prob. 21PSCh. 16.1 - Prob. 22PSCh. 16.1 - Prob. 23PSCh. 16.1 - Prob. 24PSCh. 16.1 - Prob. 25PSCh. 16.1 - Prob. 26PSCh. 16.1 - Prob. 27PSCh. 16.1 - Prob. 28PSCh. 16.1 - Prob. 29PSCh. 16.1 - Prob. 30PSCh. 16.1 - Prob. 31PSCh. 16.1 - Prob. 32PSCh. 16.1 - Prob. 33PSCh. 16.1 - Prob. 34PSCh. 16.1 - Prob. 35PSCh. 16.1 - Prob. 36PSCh. 16.1 - Prob. 37PSCh. 16.1 - Prob. 38PSCh. 16.1 - Prob. 39PSCh. 16.1 - Prob. 40PSCh. 16.1 - Prob. 41PSCh. 16.1 - Prob. 42PSCh. 16.1 - Prob. 43PSCh. 16.1 - Prob. 44PSCh. 16.1 - Prob. 45PSCh. 16.1 - Prob. 46PSCh. 16.1 - Prob. 47PSCh. 16.1 - Prob. 48PSCh. 16.1 - Prob. 49PSCh. 16.1 - Prob. 50PSCh. 16.1 - Prob. 51PSCh. 16.1 - Prob. 52PSCh. 16.1 - Prob. 53PSCh. 16.1 - Prob. 54PSCh. 16.1 - Prob. 55PSCh. 16.1 - Prob. 56PSCh. 16.1 - Prob. 57PSCh. 16.1 - Prob. 58PSCh. 16.1 - Prob. 59PSCh. 16.1 - Prob. 60PSCh. 16.2 - Prob. 1PSCh. 16.2 - Prob. 2PSCh. 16.2 - Carefully interpret each problem, restate the...Ch. 16.2 - Prob. 4PSCh. 16.2 - Prob. 5PSCh. 16.2 - Prob. 6PSCh. 16.2 - Prob. 7PSCh. 16.2 - Prob. 8PSCh. 16.2 - Prob. 9PSCh. 16.2 - Prob. 10PSCh. 16.2 - Prob. 11PSCh. 16.2 - Prob. 12PSCh. 16.2 - Prob. 13PSCh. 16.2 - Prob. 14PSCh. 16.2 - Prob. 15PSCh. 16.2 - Prob. 16PSCh. 16.2 - Prob. 17PSCh. 16.2 - Prob. 18PSCh. 16.2 - Prob. 19PSCh. 16.2 - Prob. 20PSCh. 16.2 - Problems 19-21 are patterned after Examples 8-10....Ch. 16.2 - Prob. 22PSCh. 16.2 - Prob. 23PSCh. 16.2 - Prob. 24PSCh. 16.2 - Prob. 25PSCh. 16.2 - Prob. 26PSCh. 16.2 - Prob. 27PSCh. 16.2 - Prob. 28PSCh. 16.2 - Prob. 29PSCh. 16.2 - Prob. 30PSCh. 16.2 - Prob. 31PSCh. 16.2 - Prob. 32PSCh. 16.2 - Problems 22-57 provide a variety of types of word...Ch. 16.2 - Prob. 34PSCh. 16.2 - Prob. 35PSCh. 16.2 - Prob. 36PSCh. 16.2 - Prob. 37PSCh. 16.2 - Prob. 38PSCh. 16.2 - Prob. 39PSCh. 16.2 - Prob. 40PSCh. 16.2 - Prob. 41PSCh. 16.2 - Prob. 42PSCh. 16.2 - Prob. 43PSCh. 16.2 - Prob. 44PSCh. 16.2 - Problems 22-57 provide a variety of types of word...Ch. 16.2 - Prob. 46PSCh. 16.2 - Prob. 47PSCh. 16.2 - Prob. 48PSCh. 16.2 - Prob. 49PSCh. 16.2 - Prob. 50PSCh. 16.2 - Prob. 51PSCh. 16.2 - Prob. 52PSCh. 16.2 - Prob. 53PSCh. 16.2 - Prob. 54PSCh. 16.2 - Prob. 55PSCh. 16.2 - Prob. 56PSCh. 16.2 - Prob. 57PSCh. 16.2 - Prob. 58PSCh. 16.2 - Prob. 59PSCh. 16.2 - Prob. 60PSCh. 16.3 - Prob. 1PSCh. 16.3 - IN YOUR OWN WORDS List the elementary row...Ch. 16.3 - Prob. 3PSCh. 16.3 - Prob. 4PSCh. 16.3 - Prob. 5PSCh. 16.3 - Prob. 6PSCh. 16.3 - Prob. 7PSCh. 16.3 - Prob. 8PSCh. 16.3 - Prob. 9PSCh. 16.3 - Prob. 10PSCh. 16.3 - Prob. 11PSCh. 16.3 - Prob. 12PSCh. 16.3 - Prob. 13PSCh. 16.3 - Prob. 14PSCh. 16.3 - Prob. 15PSCh. 16.3 - Prob. 16PSCh. 16.3 - Prob. 17PSCh. 16.3 - Prob. 18PSCh. 16.3 - Prob. 19PSCh. 16.3 - Prob. 20PSCh. 16.3 - Prob. 21PSCh. 16.3 - Prob. 22PSCh. 16.3 - Prob. 23PSCh. 16.3 - Prob. 24PSCh. 16.3 - Prob. 25PSCh. 16.3 - Prob. 26PSCh. 16.3 - Prob. 27PSCh. 16.3 - Prob. 28PSCh. 16.3 - Prob. 29PSCh. 16.3 - Prob. 30PSCh. 16.3 - Prob. 31PSCh. 16.3 - Prob. 32PSCh. 16.3 - Prob. 33PSCh. 16.3 - Prob. 34PSCh. 16.3 - Prob. 35PSCh. 16.3 - Prob. 36PSCh. 16.3 - Prob. 37PSCh. 16.3 - Prob. 38PSCh. 16.3 - Prob. 39PSCh. 16.3 - Prob. 40PSCh. 16.3 - Prob. 41PSCh. 16.3 - Prob. 42PSCh. 16.3 - Prob. 43PSCh. 16.3 - Prob. 44PSCh. 16.3 - Prob. 45PSCh. 16.3 - Prob. 46PSCh. 16.3 - Prob. 47PSCh. 16.3 - Prob. 48PSCh. 16.3 - Prob. 49PSCh. 16.3 - Prob. 50PSCh. 16.3 - Prob. 51PSCh. 16.3 - Prob. 52PSCh. 16.3 - Solve the systems in Problems 40-57 by...Ch. 16.3 - Prob. 54PSCh. 16.3 - Prob. 55PSCh. 16.3 - Prob. 56PSCh. 16.3 - Prob. 57PSCh. 16.3 - A winery has a large amount of a wine labeled Lot...Ch. 16.3 - Prob. 59PSCh. 16.3 - A candy maker mixes chocolate, milk, and mint...Ch. 16.4 - Prob. 1PSCh. 16.4 - Prob. 2PSCh. 16.4 - Prob. 3PSCh. 16.4 - Prob. 4PSCh. 16.4 - Prob. 5PSCh. 16.4 - Prob. 6PSCh. 16.4 - Prob. 7PSCh. 16.4 - Prob. 8PSCh. 16.4 - Prob. 9PSCh. 16.4 - Prob. 10PSCh. 16.4 - Prob. 11PSCh. 16.4 - Prob. 12PSCh. 16.4 - Prob. 13PSCh. 16.4 - Prob. 14PSCh. 16.4 - Prob. 15PSCh. 16.4 - Prob. 16PSCh. 16.4 - Prob. 17PSCh. 16.4 - Prob. 18PSCh. 16.4 - Prob. 19PSCh. 16.4 - Prob. 20PSCh. 16.4 - Prob. 21PSCh. 16.4 - Prob. 22PSCh. 16.4 - Prob. 23PSCh. 16.4 - Prob. 24PSCh. 16.4 - Prob. 25PSCh. 16.4 - Prob. 26PSCh. 16.4 - Prob. 27PSCh. 16.4 - Prob. 28PSCh. 16.4 - Prob. 29PSCh. 16.4 - Prob. 30PSCh. 16.4 - Prob. 31PSCh. 16.4 - Prob. 32PSCh. 16.4 - Prob. 33PSCh. 16.4 - Prob. 34PSCh. 16.4 - Prob. 35PSCh. 16.4 - Prob. 36PSCh. 16.4 - Prob. 37PSCh. 16.4 - Prob. 38PSCh. 16.4 - Prob. 39PSCh. 16.4 - Prob. 40PSCh. 16.4 - Prob. 41PSCh. 16.4 - Prob. 42PSCh. 16.4 - Prob. 43PSCh. 16.4 - Prob. 44PSCh. 16.4 - Prob. 45PSCh. 16.4 - Prob. 46PSCh. 16.4 - Prob. 47PSCh. 16.4 - Prob. 48PSCh. 16.4 - Prob. 49PSCh. 16.4 - Prob. 50PSCh. 16.4 - Prob. 51PSCh. 16.4 - Prob. 52PSCh. 16.4 - Prob. 53PSCh. 16.4 - Prob. 54PSCh. 16.4 - Prob. 55PSCh. 16.4 - Prob. 56PSCh. 16.4 - Prob. 57PSCh. 16.4 - Prob. 58PSCh. 16.4 - Prob. 59PSCh. 16.4 - Prob. 60PSCh. 16.5 - Prob. 1PSCh. 16.5 - Prob. 2PSCh. 16.5 - Prob. 3PSCh. 16.5 - Prob. 4PSCh. 16.5 - Prob. 5PSCh. 16.5 - Prob. 6PSCh. 16.5 - Prob. 7PSCh. 16.5 - Prob. 8PSCh. 16.5 - Prob. 9PSCh. 16.5 - Prob. 10PSCh. 16.5 - Prob. 11PSCh. 16.5 - Prob. 12PSCh. 16.5 - Prob. 13PSCh. 16.5 - Prob. 14PSCh. 16.5 - Prob. 15PSCh. 16.5 - Prob. 16PSCh. 16.5 - Prob. 17PSCh. 16.5 - Prob. 18PSCh. 16.5 - Prob. 19PSCh. 16.5 - Prob. 20PSCh. 16.5 - Prob. 21PSCh. 16.5 - Prob. 22PSCh. 16.5 - Prob. 23PSCh. 16.5 - Prob. 24PSCh. 16.5 - Prob. 25PSCh. 16.5 - Prob. 26PSCh. 16.5 - Prob. 27PSCh. 16.5 - Prob. 28PSCh. 16.5 - Prob. 29PSCh. 16.5 - Prob. 30PSCh. 16.5 - Prob. 31PSCh. 16.5 - Prob. 32PSCh. 16.5 - Prob. 33PSCh. 16.5 - Prob. 34PSCh. 16.5 - Prob. 35PSCh. 16.5 - Prob. 36PSCh. 16.5 - Prob. 37PSCh. 16.5 - Prob. 38PSCh. 16.5 - Prob. 39PSCh. 16.5 - Prob. 40PSCh. 16.5 - Prob. 41PSCh. 16.5 - Prob. 42PSCh. 16.5 - Prob. 43PSCh. 16.5 - Prob. 44PSCh. 16.5 - Prob. 45PSCh. 16.5 - Prob. 46PSCh. 16.5 - Prob. 47PSCh. 16.5 - Prob. 48PSCh. 16.5 - Prob. 49PSCh. 16.5 - Prob. 50PSCh. 16.5 - Prob. 51PSCh. 16.5 - Prob. 52PSCh. 16.5 - Prob. 53PSCh. 16.5 - Prob. 54PSCh. 16.5 - Prob. 55PSCh. 16.5 - Solve the linear programming problems in Problems...Ch. 16.5 - Prob. 57PSCh. 16.5 - Prob. 58PSCh. 16.5 - Prob. 59PSCh. 16.5 - Prob. 60PSCh. 16.CR - Prob. 1CRCh. 16.CR - Prob. 2CRCh. 16.CR - Prob. 3CRCh. 16.CR - Prob. 4CRCh. 16.CR - Prob. 5CRCh. 16.CR - Prob. 6CRCh. 16.CR - Prob. 7CRCh. 16.CR - Prob. 8CRCh. 16.CR - Prob. 9CRCh. 16.CR - Prob. 10CRCh. 16.CR - Prob. 11CRCh. 16.CR - Prob. 12CRCh. 16.CR - Prob. 13CRCh. 16.CR - Prob. 14CRCh. 16.CR - Prob. 15CRCh. 16.CR - Prob. 16CRCh. 16.CR - Prob. 17CRCh. 16.CR - Prob. 18CRCh. 16.CR - Prob. 19CRCh. 16.CR - Prob. 20CR
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