Question about Linear Algebra

Suppose v1, v2, v3 is a basis for R3 and that A is a 3x3 matrix.

a. Show that {Av1,Av2,Av3} is linearly independent.

b. Show that if b is any vector in R3 then span (Av1,Av2,Av3) contains b.

c. What is it that we just proved in the above exercises?




I don't even know where to begin (Crying) I appreciate any help! (Nod)

Quote:

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Originally Posted by nicolem1051

Suppose v1, v2, v3 is a basis for R3 and that A is a 3x3 matrix.

a. Show that {Av1,Av2,Av3} is linearly independent.


This is false without one very special condition on the matrix A; for example, take A to be the zero matrix.


b. Show that if b is any vector in R3 then span (Av1,Av2,Av3) contains b.

As above

Tonio

c. What is it that we just proved in the above exercises?





I don't even know where to begin (Crying) I appreciate any help! (Nod)

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