   Chapter 11.4, Problem 53E ### 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. { 3 y + 5 z = 4 2 x         −   z = 10 4 x + 7 y         = 0

To determine

To solve:

The system of equation {3y+5z=42xz=104x+7y=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 {3y+5z=42xz=104x+7y=0.

The matrix D is the coefficient matrix.

|D|=|035201470|=03|2140|+5|2047|=58(1)

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

|Dx|=|4351001070|=4|0170|3|10100|+5|10007|=4(0+7)3(00)+5(700)=378(2)

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

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