   Chapter 11.4, Problem 56E ### 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 = 1 y + z = 2 z + w = 3 w − x = 4

To determine

To solve:

The system of equation {x+y=1y+z=2z+w=3wx=4 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=1y+z=2z+w=3wx=4.

The matrix D is the coefficient matrix.

|D|=|1100011000111001|=1|110011001|1|010011101|=1+1=2(1)

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

|Dx|=|1100211030114001|=1|110011001|1|210311401|=11(2+1)=2(2)

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

|Dy|=|1100021003111401|=1|210311401|1|010011101|=1(2+1)+1=4(3)

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

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