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Chapter 6: Q9E (page 289)

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

9. [1111112222113331114411115]

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=1111112222113331114411115

03

To find determinant by using Gaussian Eliminations

We multiply the first row by -1 and add it to every other row.

We get,

A=1111111111002220003300004

We had zero row interchanges, so

detA=-1掳.1.1.2.3.4detA=24.

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Most popular questions from this chapter

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

22.T(f(t))=f(-t)fromPntoPn

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

23.L(A)=ATfrom鈩�n脳nto鈩�n脳n

In Exercises 62 through 64, consider a function from to that is linear in both columns and alternating on the columns. See Examples 4 and 6 and the subsequent discussions. Assume that .


64. Using Exercises 62 and 63 as a guide, show that D(A)=ad-bc=detAfor all 2脳2matrices A .

det(4A)=4detAfor all4脳4 matricesA.

Show that A(adjA)=0=(adjA)Afor all noninvertible n脳nmatrices A. See Exercise 42.
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