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Chapter 11: Q. 73 (page 756)

Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.

25x+61y-12z=2118x-12y+7z=73x+4y-z=-2

Short Answer

Expert verified

On solving the system of equations, we get,

x=-1.1,y=2.5,z=8.3

Step by step solution

01

Step 1. Given information.

Consider the given question,

25x+61y-12z=2118x-12y+7z=73x+4y-z=-2

02

Step 2. Assume the equations.

Consider the given question and assume,

A=2561-1218-12734-1,X=xyzB=217-2

The original system of equations can be written compactly as the matrix equation. Then,

AX=B......(i)

03

Step 3. Find the inverse matrix.

We need to find the inverse matrix of A,

A-1=-0.020.020.410.060.02-0.570.160.12-2.05

Multiply each side of equation (i) by A-1,

data-custom-editor="chemistry" A-1AX=A-1BA-1AX=A-1BI3X=A-1BX=A-1B......(ii)

Use equation (ii) to findX. This can be done using the graphing utility.

On enter the matrices A and B into a graphing utility, we get,

x=-1.1,y=2.5,z=8.3

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