   Chapter 11.CR, Problem 69E ### 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

# 6 7 − 7 0 . Using Cramer’s Rule to solve a system: Solve the system using Cramer’s Rule. { 2 x − y + 5 z = 0 − x + 7 y = 9 5 x + 4 y + 3 z = − 9

To determine

To solve:

The system of equation {2xy+5z=0x+7y=95x+4y+3z=9 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 {2xy+5z=0x+7y=95x+4y+3z=9.

The matrix D is the coefficient matrix.

|D|=|215170543|=2|7043|(1)|1053|+5|1754|=423195=156 ……(1)

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

|Dx|=|015970943|=0(1)|9093|+5|9794|=0+27+495=522 ……(2)

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

|Dy|=|205190593|=2|9093|0+5|1959|=540+180=126 ……(3)

The matrix Dz is obtained by replacing the third columns of D by the constant terms

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