   Chapter 11.2, Problem 64E ### 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

# Discuss: Square Root of Matrices A square root of a matrix B is a matrix A with the property that A 2 = B . (This is the same definition as for a square root of a number.) Find as many square roots as you can of each matrix: [ 4 0 0 9 ] [ 1 5 0 9 ] [Hint: If A = [ a b c d ] , write the equation that a , b , c and d would have to satisfy if A is the square root of the given matrix.]

To determine

To find:

The square root of the matrices  and .

Explanation

Approach:

Two matrices A and B can be multiplied if and only if the number of columns in A is same as the number of rows in B.

If A=[aij] is an m×n matrix and B=[bij] an n×k matrix, then their product in the m×k matrix C=[cij].

Calculations:

Consider the matrix .

Let A1=[abcd] be the square root of the matrix .

Therefore, the elements of A1 is calculated below.

A12=[abcd][abcd]=[aa+bcab+bdca+dccb+dd]=[a2+bcab+bdac+dcbc+d2]

Compare the obtained results with the given matrix.

[a2+bcab+bdac+dcbc+d2]=

The following equations are formed from the above obtained results.

a2+bc=4(1)

ab+bd=0(2)

ac+dc=0(3)

d2+bc=9(4)

Solving the above equations results a=±2, b=0, c=0 and d=±3.

Therefore, the square root of the matrix  is A1= or A1=.

Consider the matrix 

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