- #1

succubus

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Consider a 5 x 4 matrix...

We are told that the vector,

1

2

3

4

is in the kernel of A. Write

v4

as a linear combination of

v1,v2,v3I'm a bit confused. Since this is a kernel of A, the kernel is a subset of R^m, therefore the other columns are linear combinations and therefore redundant. (since this is the only column represented) So, that means I can have the columns be anything I want, so why can't they just all be the same? Is this too easy or am I missing something?

We are told that the vector,

1

2

3

4

is in the kernel of A. Write

v4

as a linear combination of

v1,v2,v3I'm a bit confused. Since this is a kernel of A, the kernel is a subset of R^m, therefore the other columns are linear combinations and therefore redundant. (since this is the only column represented) So, that means I can have the columns be anything I want, so why can't they just all be the same? Is this too easy or am I missing something?

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