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Chapter 6: Q 6.3-9E (page 306)

Short Answer

Expert verified

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.

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 find the relationship between them.

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Most popular questions from this chapter

det(4A)=4detAfor all4脳4 matricesA.

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

21.T(f(t))=f(-t)fromP3toP3

IfA is a 4脳4 matrix whose entries are all 1 or -1 , then detAmust be divisible by 8 (i.e., detA=8kfor some integer k).

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

det(A+B)=detA+detBfor all5脳5 matricesA andB.
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