   Chapter 11.4, Problem 48E ### 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. { 5 x − 3 y + z = 6 4 y − 6 z = 22 7 x + 10 y       = − 13

To determine

To solve:

The system of equation {5x3y+z=64y6z=227x+10y=13 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 {5x3y+z=64y6z=227x+10y=13.

The matrix D is the coefficient matrix.

|D|=|5310467100|=5|46100|(3)|0670|+1|04710|=5(0+60)+3(0+42)+1(028)=398(1)

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

|Dx|=|631224613100|=6|46100|(3)|226130|+1|2241310|=360234+272=398(2)

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

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