   Chapter 11.CR, Problem 70E ### 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. { 3 x + 4 y − z = 10 x − 4 z = 20 2 x + y + 5 z = 30

To determine

To solve:

The system of equation {3x+4yz=10x4z=202x+y+5z=30 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 {3x+4yz=10x4z=202x+y+5z=30.

The matrix D is the coefficient matrix.

|D|=|341104215|=3|0415|4|1425|+(1)|1021|=12521=41 ……(1)

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

|Dx|=|104120043015|=10|0415|(4)|204305|+(1)|200301|=4088020=860 ……(2)

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

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