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Chapter 6: Q16E (page 306)

True or false? If惟is a parallelogram in R3 .And T(x鈫�)=Ax鈫� is a linear transformation fromR3 to R3 , then area of T(惟)=|detA|(area of惟).

Short Answer

Expert verified

Therefore, the given condition is false.

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

To check the given condition is true or false. 

Let惟be a parallelepiped formed bye鈫�1ande鈫�2 .

Clearly it's a rectangle, whose area is 1.2=2 .

Let T be the linear transformation defined by A=2l3.

Then, T(惟)is a rectangle formed by 3e鈫�1 and 6e鈫�2.

According to the formula Area=b脳h

However, its area is 3.6=18鈮�54=27.2=detA.1.2.

Therefore, the given condition is false.

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