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Chapter 6: Q2E (page 305)

Find the area of the triangle defined by [37]and[82].

Short Answer

Expert verified

Therefore, the Area of triangle is 25 .

Step by step solution

01

Definition. 

Basically, it is equal to half of the Area of the parallelogram.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

A=1/2脳b脳h

02

Given. 

Given Matrix,

37

And

82

03

To find the area of the triangle.

Since the area of a triangle formed by two vectors is equal to half the area of a parallelogram formed by the same vectors, we compute

12det3872=12.50dett3872=25

Therefore,

Area of triangle is 25 .

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Most popular questions from this chapter

Consider those 4脳4matrices whose entries are all 1 , -1 , or 0 . What is the maximal value of the determinant of a matrix of this type? Give an example of a matrix whose determinant has this maximal value.

Which of the following functions F of A=[abcd] are linear in both columns? Which are linear in both rows? Which are alternating on the columns?
role="math" localid="1659502796300" a.F(A)=bcb.F(A)=cdc.F(A)=acd.F(A)=bc-ade.F(A)=c

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

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Find all 2x2matrices for which [23]is an eigenvector with associated eigenvalue -1.
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