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Chapter 6: Q2E (page 265)

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

2.[123168-2-40]

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=[123168-2-40]

03

To find determinant by using Gaussian Eliminations

First, we multiply the first row by -1 and add it to the second row. Then, we multiply the first row by 2 and add it to the third row.

We get,

A=123045006

We had zero row swaps, so

role="math" localid="1659503688412" detA=(-1)0.1.4路6detA=24

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Most popular questions from this chapter

Find the determinants of the linear transformations in Exercises 17 through 28.

19.T(f)=2f+3f'fromP2toP2

If a square matrix A is invertible, then its classical adjoint adj(A) is invertible as well.

Find the determinants of the linear transformations in Exercises 17 through 28.

27. T(f)=af'+bf", where a and b are arbitrary constants, from the space V spanned by cos(x)and sin(x)to V

If an n脳n matrixAis invertible, then there must be an (n-1)脳(n-1)sub matrix of(obtained by deleting a row and a column of) that is invertible as well.

If all the entries of a square matrixAare integers and detA=1 , then the entries of matrix A-1 must be integers as well.
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