   Chapter 11.CT, Problem 19CT ### 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

# Solve using Cramer’s rule: { 2 x           − z = 14 3 x −     y + 5 z =   0 4 x +   2 y + 3 z = − 2

To determine

To find:

The solution of the system {2xz=143xy+5z=04x+2y+3z=2 using Cramer’s rule.

Explanation

Approach:

If a system of 3 linear equations in the 3 variable x,y,z is equivalent to the matrix equation DX=B, and if D0, then its solutions are

x=|Dx||D|,y=|Dy||D|,z=|Dz||D|

Here, Dx,Dy,andDz are the matrices obtained by replacing the 1st, 2nd, and 3rd column of D by the n×1 matrix B respectively.

Calculation:

The system of equations {2xz=143xy+5z=04x+2y+3z=2 is equivalent to the matrix equation DX=B.

Here, D=, X=[xyz], and B=.

|D|=|201315423|=2(13)0110=36

|Dx|=|1401015223|=14(13)010+(1)(2)=180

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