- #1

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## Homework Statement

Show that A

**x**=

**b**has a solution if and only if

**b**is in CS(A).

## Homework Equations

## The Attempt at a Solution

A

**x**=

**b**

b [tex]\in[/tex] CS(A) means

d1A1 + d2A2+ .........+ dnAn = b

and I am lost

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- Thread starter Maxwhale
- Start date

- #1

- 35

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Show that A

A

b [tex]\in[/tex] CS(A) means

d1A1 + d2A2+ .........+ dnAn = b

and I am lost

- #2

- 329

- 1

Let's go back to basics. What is the definition of Column space?

- #3

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the subspace of Rn spanned by the column vectors of A

- #4

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1)Assume Ax = b has a solution, then b can be written as a linear combination with the vectors from the columns of A. Since the span is the linear combination of the vectors a1 a2 a3 ... an then b is in the span. So then use your definition.

2)Now work the other way. Assume b is in Col A, and work towards showing that Ax = b has a solution because of that.

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