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Chapter 6: Q1E (page 308)

If Bis obtained be multiplying a column ofA by9 , then the equation detB=9detAmust hold.

Short Answer

Expert verified

Therefore, the given condition is true.

Step by step solution

01

Definition

A determinant is a unique number associatedwith a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

02

To check whether the given condition is true or false

By using the Laplace expansion along said column of,

We get:

A=1001detA=1-0detA=1

B=9001detB=9-0detB=9

role="math" localid="1664185768735" detB=9detA1 = 9(1)

Therefore, the given condition is true by using the Laplace expansion

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Most popular questions from this chapter

There exist real invertible 3脳3 matrices A andSsuch that STAS=-A

In an economics text11we find the following system:

[-R1R1-1-伪伪1-伪-1-伪2R2-R2-1-伪2伪][dx1dy1dp]=[00-R2de2].

Solve for dx1,dy1, and dp. In your answer, you may refer to the determinant of the coefficient matrix as D. (You need not compute D.) The quantitiesR1,R2and D are positive, and ais between zero and one. If de2is positive, what can you say about the signs of dy1and dp?

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 all the entries of a 7脳7matrix A are 7, then detA must be 77.

IfA is an n脳n matrix of rank n-1, what is the rank of adj(A)? See Exercises 42 and 43.

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