   Chapter 11.4, Problem 55E ### 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. { x + y + z + w = 0 2 x             + w = 0 y − z       = 0 x       + 2 z       = 1

To determine

To solve:

The system of equation {x+y+z+w=02x+w=0yz=0x+2z=1 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 {x+y+z+w=02x+w=0yz=0x+2z=1.

The matrix D is the coefficient matrix.

|D|=|1111200101101020|Expandingby2ndrow.=2|111110020|+0+0+1|111011102|=4(1)

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

|Dx|=|0111000101101000|Expandingby2ndrow.=1|011011100|=2(2)

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

|Dy|=|1011200100101121|Expandingby2ndrow.=2|011010120|+1|101001112|=2+1=1(3)

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

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 