   Chapter 11.4, Problem 54E ### 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 x − 5 y       = 4 x + y − z = 8 3 x       + 5 z = 0

To determine

To solve:

The system of equation {2x5y=4x+yz=83x+5z=0 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 {2x5y=4x+yz=83x+5z=0.

The matrix D is the coefficient matrix.

|D|=|250111305|=2|1105|+5|1135|+0=2(50)+5(5+3)=50(1)

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

|Dx|=|450811005|=4|1105|(5)|8105|+0=4(50)+5(40)=220(2)

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

|Dy|=|240181305|=2|8105|4|1135|+0=2(40)4(5+3)=48(3)

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

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