1-Consider the following matrixA:

1 1 3

A= ( -3 -1 -7 )

-3 -5 -8

2 -1 1

For each of the following vectors, determine whether the vector is in the image ofA. If so, demonstrate this by providing a vectorxso thatAx=b_i.

-1 7 -8

b₁= ( 5 ) b₂= ( -13 ) b₃= ( -9 )

1 -23 -1

-5 -2 10

2-Consider the following vectors:

3 3 -6

a= ( - 2 ) b= ( -1 ) c= ( 7 )

2 3 4

- 1 -3 -7

For each of the following vectors, determine whether it is in span{a,b,c}. If so, express it as a linear combination usinga,b, andcas the names of the vectors above.

9 -6 -4

v₁ =( -7 ) v₂=( 7 ) v₃= ( 3 )

0 4 -7

2 -7 4

3-Given the following vectorsuandv, find a vectorwin³so that{u,v,w}spans³and a non-zero vectorzin³so that{u,v,z}does not span³.

8 7

u= ( 6 ) v= ( 7 )

9 1