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Chapter 6: Q5E (page 289)

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

5.[0234000412340034]

Short Answer

Expert verified

Therefore, the determinant of given matrix is given by,

detA=-24

Step by step solution

01

Definition

Gaussian elimination method is used to solve a system of linear equations.


Gaussian elimination provides a relatively efficient way of constructing the inverse to a matrix.


Interchanging two rows. Multiplying a row by a constant (any constant which is not zero).

02

Given

Given Matrix,

A=[0234000412340034]

03

To find determinant by using Gaussian Eliminations

First, we switch the first and third row.

We get,

A1=1234000402340034

Then, we switch the second and third row.

We get,

A2=1234023400040034

Lastly, we switch the third and fourth row.

We get

A3=1234023400340034

We had three row interchanges, so

detA=(-1)3.1.2.3.4detA=-24.

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