   Chapter 11.4, Problem 50E ### 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

# 4 1 - 5 6 Cramer’s Rule Use Cramer’s Rule to solve the system. { − 2 a         + c = 2 a + 2 b −   c = 9 3 a + 5 b + 2 c = 22

To determine

To solve:

The system of equation {2a+c=2a+2bc=93a+5b+2c=22 using Cramer’s rule.

Explanation

Approach:

The Cramer’s rule for the system in three variables is given below,

If a system of n linear equations in the n variable x1, x2,…, xn is equivalent to the matrix equation DX=B, and if |D|0, then its solutions are given below.

x1=|Dx1||D|, x2=|Dx2||D|,………, xn=|Dxn||D|

The matrix Dxi is obtained by replacing the ith column of D by the n×1 matrix B.

Calculation:

Consider the system of equations, {2a+c=2a+2bc=93a+5b+2c=22.

The matrix D is the coefficient matrix.

|D|=|201121352|=2|2152|+0+1|1235|=2(4+5)+56=19(1)

The matrix Da is obtained by replacing the first columns of D by the constant terms.

|Da|=|2019212252|=2|2152|+0+1|92225|=2(4+5)+(4544)=19(2)

The matrix Db is obtained by replacing the second columns of D by the constant terms.

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