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Chapter 6: Q 6.3-13E (page 306)

Question:Find the area (or 2-volume) of the parallelogram (or 2parallelepiped) defined by the vectors

and

Short Answer

Expert verified

Therefore, the area of the parallelogram of the vectors is given by,

Step by step solution

01

Definition. 

The area of a parallelogram is the number of square units inside the polygon.

The area of a parallelogram can be determined by multiplying the base and height.

For finding the area of a parallelogram, the base and height must be perpendicular. The area of a parallelogram is given by,

Area = b 脳 h

02

Given. 

Given Matrix,

and

03

To find area of the parallelogram of the vectors.

These two vectors form the matrix

Therefore, the area is

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Most popular questions from this chapter

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 .

Consider a 4x4 matrix A with rows V1鈫�,V2鈫�,V3鈫�,V4鈫�. If det(A) = 8, find the determinants in Exercises 11 through 16.

16. role="math" localid="1659506283449" det[6v鈬赌1+2v鈬赌4v鈬赌2v鈬赌33v鈬赌1+v鈬赌4]

Find all 2脳2 matrices Asuch thatadj(A)=AT.

There exist real invertible 3脳3 matrices A andSsuch thatS-1AS=2A .

If an n脳n matrixAis invertible, then there must be an (n-1)脳(n-1)sub matrix of(obtained by deleting a row and a column of) that is invertible as well.
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