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Linear Algebra With Applications
Found in: Page 22
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

a. Find all solutionsx1,x2,x3,x4 of the system .


b. In partrole="math" localid="1659677484607" (a) , is there a solution with x1=1andx4=13 ?

a. For arbitrary x3 and x4 , x1=3x32x4,x2=2x3x4

b. Yes, x1=1,x2=5,x3=9,x4=13

See the step by step solution

Step by Step Solution

(a)Step 1: Consider the equations to find other equations

Find the expression for, x1.

x2=12(x1+x3)2x2=x1+x3x1=2x2x3       ......(1)

Find the expression for, x2 .

x3=12(x2+x4)2x3=x2+x4x2=2x3x4           ......(2)

Step 2: Express the variable in terms of other variables

Re-write x1in terms of x3andx4 .

x1=2x2x3x1=2(2x3x4)x3=3x32x4       ......(3)

Therefore, x1=3x32x4,x2=2x3x4

(b)Step 3: Using the above equations, find the values of the variables

Consider the given values of the variables.

x1=1 and x4=13

Substitute these values in the above equations to find the values of the remaining variables.

Consider the equation (3).


Consider the equation (2).


Therefore, x1=1,x2=5,x3=9,x4=13.

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