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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

Question:We say that a linear transformation Tfrom N3toN3to preserves orientation if it transforms any positively oriented basis into another positively oriented basis. See Exercise 19. Explain why a linear transformationT(x鈫�)=Ax鈫�preserves orientation if (and only if) detAis positive.

If Ais any n x n matrix, thendet(AAT)=det(ATA).

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 .

If all the diagonal entries of an n脳nmatrix Aare odd integers and all the other entries are even integers, thenA must be an invertible matrix.

There exist real invertible 3脳3 matrices A and S such that .

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