Let A be a 3x4 matrix. If b=a1+a2+a3+a4. what can you conclude about the number of solutions to the linear system Ax=b?

Question

blockcolder · Answer

What's a1, a2, a3, a4?

goformit100 · Answer

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amistre64 · Answer

a1 a2 a3 a4 are the column vectors of A

amistre64 · Answer

since A is a 3row x 4col  matrix, its going to have to have a zero determinant i believe

amistre64 · Answer

... but if could rref out to say:

1 0 0 0 s
0 1 0 0 t
0 0 1 0 r

blockcolder · Answer

But non-square matrices have no determinants.
On the other hand, if b=a1+a2+a3+a4, then this means b lies in the column space of A.