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Chapter 6: Q 6.3-11E (page 306)

Short Answer

Expert verified

Therefore, the determinant of given linear transformation is given by,

detA= detT = 12

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

Given. 

Consider the linear transformation,

03

To find det A.

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Most popular questions from this chapter

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?

What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.

There exists a 4脳4 matrix whose entries are all 1or -1 , and such thatdetA=16.

Explain why any patternPin a matrixA, other than the diagonal pattern, contains at least one entry below the diagonal and at least one entry above the diagonal.

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

positive or negative? How can you tell? Do not use technology.
See all solutions

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