Consider the matrix A and vector b given below: ^= [ A 3 -1 -1 1 -1 3 2 -8 b Is b in the span of the columns of A? . Does Ax = b have a solution? If so, state the solution (in parametric vector form). If not, why not? • Does Ax = 0 have a nontrivial solution? Why or why not? • Does Ax = b have a solution for any b E R³? Why or why not?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the matrix A and vector b given below:
4-13
A
-1
-1 3
-1 2 -8
b=
Is b in the span of the columns of A?
. Does Ax = b have a solution? If so, state the solution (in parametric
vector form). If not, why not?
• Does Ax = 0 have a nontrivial solution? Why or why not?
• Does Ax = b have a solution for any b E R³? Why or why not?
Transcribed Image Text:Consider the matrix A and vector b given below: 4-13 A -1 -1 3 -1 2 -8 b= Is b in the span of the columns of A? . Does Ax = b have a solution? If so, state the solution (in parametric vector form). If not, why not? • Does Ax = 0 have a nontrivial solution? Why or why not? • Does Ax = b have a solution for any b E R³? Why or why not?
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