So the question asks,
Let A=
[5 8 7]
[0 1 -1]
[1 3 0]
and let vector u=
[2]
[-3]
[2]
Is vector u, in the span of the columns of A?
I'm hopelessly lost here, I have no idea what to do, an answer would be very much appreciated but even more so would be the steps to find it. Thanks
Let A=
[5 8 7]
[0 1 -1]
[1 3 0]
and let vector u=
[2]
[-3]
[2]
Is vector u, in the span of the columns of A?
I'm hopelessly lost here, I have no idea what to do, an answer would be very much appreciated but even more so would be the steps to find it. Thanks
-
7
-1
0 is in the spanning set of 5 8
0 1
1 3.
Then we add 5a+8b=2
b = -3. If 2,-3,2 is in the span, then the third component would evaluate to a+3b=2.
b = -3 => a = 26/5. Then a+3b = 26/5-9 = -19/5 =/= 2.
Hence, the vector is not in the span.
-1
0 is in the spanning set of 5 8
0 1
1 3.
Then we add 5a+8b=2
b = -3. If 2,-3,2 is in the span, then the third component would evaluate to a+3b=2.
b = -3 => a = 26/5. Then a+3b = 26/5-9 = -19/5 =/= 2.
Hence, the vector is not in the span.