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Chapter 2: Q52E (page 109)

Question: TRUE OR FALSE?

If T is any linear transformation from鈩�3to鈩�3 , thenT(v鈫�脳w鈫�)=T(v鈫�)脳T(w鈫�)for all vectors v鈫� andw鈫�in鈩�3.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Consider the parameters

Irrespective of the order of the system of matrices, the product of these matrices is said to be commutative.

Consider the linear transformation,T鈭�鈩�3

Consider the vectors,,v鈫�,w鈭�鈩�3鈫�

The cross-product of vectors results in vectors.

Irrespective of the operation performed on the vectors, that is, computation of the transformation of the product of vectors or the product of transformed vectors results in the same output.

02

Conclusion

Hence, the given statement is true.

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Most popular questions from this chapter

Give a geometric interpretation of the linear transformations defined by the matrices in Exercises16through 23. Show the effect of these transformations on the letter L considered in Example5. In each case, decide whether the transformation is invertible. Find the inverse if it exists, and interpret it geometrically. See Exercise13

[1000]

TRUE OR FALSE?

If the linear system A2x鈫�=b鈫� is consistent, then the systemrole="math" localid="1659352762883" Ax鈫�=b鈫� must be consistent as well.

Question: Consider the matrix A2 in Example 4 of Section 2.3.

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TRUE OR FALSE?

There exists a real number k such that the matrix [k-23-3k-2]fails to be invertible.

Which of the functions f from R toR in Exercises 21 through 24 are invertible?22 f(x)=2x.
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