   Chapter 11.3, Problem 2E ### 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

# 2 . (a) Write the following system as a matrix equation A X = B . System Matrix equation A · X = B 5 x + 3 y = 4 3 x + 2 y = 3 [ _ _ _ _ ] [ _ _ ] = [ _ _ ] (b) The inverse of A is A − 1 = [ _ _ _ _ ] .(c) The solution of the matrix equation is X = A − 1 B X = A − 1 . B [ x y ] = [ _ _ _ _ ] [ _ _ ] (d) The solution of the system is x = ________, y = ________.

To determine

(a)

To convert:

To convert the system of linear equations

5x+3y=43x+2y=3

into the system of matrix equation.

Explanation

Approach:

Two matrices A and B can be multiplied if they satisfy the condition that the number of columns in A is same as the number of rows in B.

Two matrices A and B are said to be equal if the matrices have the same dimensions and each element of A is equal to the corresponding element of B.

Calculation:

If we write the left-hand and right-hand sides of both linear equations as elements of matrices and equate them, we get:

[5x+3y3x+2y]=[xy]=

Hence, the system of linear equation

5x+3y=43x+2y=3

is converted into the system of matrix equation as follows

To determine

(b)

To find:

To find the inverse of the matrix A.

To determine

(c)

To find:

To find the solution of the given system of linear equations by matrix method.

To determine

(d)

To fill:

The blanks in the statement “The solution of the system is x=________, y=________”.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 