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Chapter 2: Q56 E (page 86)

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation.

X=1235=l2

Short Answer

Expert verified

The matrix X that will satisfy the equation will be-523-1

Step by step solution

01

Assuming the matrix

Since, the product of matrix gives 2脳2matrix then the order of matrix X should be 2脳2

Let the matrix beX=acbd .

We know the matrixI2=1001

Then the equation will become

acbd1235=1001

02

Solving the Matrix

For solving the given matrix equation first of multiply the left hand side matrix.

a+3b2a+5cb+3d2b+5d=1001

Now equating the left-hand and right-hand matrix.

a+3c=12a+5c=0b+3d=02a+5d=1

On solving the above equations, we will get:

a=-5,b=3,c=2,d=-1

Hence, the matrix X that will satisfy the equation will be-523-1-523-1

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Most popular questions from this chapter

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

24. [0-110]

TRUE OR FALSE?

There exists a real number k such that the matrix [k-23-3k-2]fails to be invertible.

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

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