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linear algebra (v. simple)

I'm guessing that I just don't understand the question,

Determine if the vector b is in the span of the columns of the matrix A.
(what's getting me is what they mean by 'of the columns'?)

Here's the question:

A quick demo would be useful... (answer is 'yes' btw, presuming that it means, "yes, the vector b is in the span of the columns of the matrix A.").

Reply 1

dvs

b is in the span of the columns of A if it can be written as a linear combination of them, in this case:


b = 5 = -4 * 1  + (9/2) * 2
    6        3            4

Which you can find by solving a pair of simultaneous equations (i.e. the equations whose coefficient matrix is [A|b]).

Reply 2

W@t3R

yey, cool.....

One more quick thing,

c1, c2, and c3 are scalars such that c1A1 + c2A2 + c3A3 = B. Thus,
(see pic).

How did they get the left hand side? :confused:

Reply 3

dvs

Perhaps you should look up how matrices are added and multiplied by scalars.

Reply 4

W@t3R

dvs

Perhaps you should look up how matrices are added and multiplied by scalars.

I have

....
It's just not clicking, I don't know why.... :frown:

Matrices are added together by added the individual entries (not defined of the matrices are of different sizes). Scalar multiplication is done pretty much the same way.....

:frown:

.........

Reply 5

dvs

The first matrix becomes
0 ........ c_1
-c_1 ... 0

The second becomes
c_2 ... 0
0 ...... c_2

And the third becomes
c_3 ... c_3
c_3 ... c_3

Now add them up...

Reply 6

W@t3R