   Chapter 11.CR, Problem 59E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 5 3 − 6 0 . Determinants and Inverse Matrices: Find the determinant and, if possible, the inverse of the matrix. [ 1 0 0 1 0 2 0 2 0 0 3 3 0 0 0 4 ]

To determine

To find:

The determinant of the matrix , and the inverse, if it exists.

Explanation

Approach:

Take a 4×8 matrix with left half as matrix B and right half as I4 and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix B.

Calculation:

Consider the determinant A=|1001020200330004|.

Expand the determinant by fourth row.

det(A44)=|100020003|=1(1)1+1|2003|=1(2300)=6

det(A)=0(1)4+1A41+0(1)4+2A42+0(1)4+3A43+4(1)4+46=0+0+0+24=24

Since, det(A)0, the inverse of the matrix exists.

Inverse of the matrix is shown below:

Consider a matrix, [1001020200330004|1000010000100001]

Perform the transformation R212R2.

[10010(12)2(12)0(12)2(12)00330004|10000(12)1(12)0(12)0(12)00100001][1001010100330004|10000120000100001]

Perform the transformation R313R3.

[100101010(13)0(13)3(13)3(13)0004|1000012000(13)0(13)1(13)0(13)0001][1001010100110004|100001200001300001]

Perform the transformation R414R4.

[1001010100110(14)0(14)0(14)4(14)|100001200001300(14)0(14)0(14)1(14)][1001010100110001|1000012000013000014]

Perform the transformation R1R1R4

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