Express each column vector of AA as a linear combination of the column vectors of A

[frctl]

Express each column vector of AA as a linear combination of the column vectors of A

x

After multiplying I obtain the matrix:
[ -3 12 76 ]
48 29 98
24 56 97

Don't know how to answer this question..

 

[Steven G]

Pick a column of AA, say the 1st column. Now using the three columns of A write the 1st column of AA as a linear combination of the columns in A

That is find r, s and t such that Column 1 of AA = r*Column 1 of A + s*Column 2 of A + t*Column 3 of A
Do the same for the other two columns

 

[frctl]

The equations I obtain are:
-3r + 48r + 24r
12s +29s + 56s
76t + 98t + 97t

Is this correct?

 

[Otis]

The equations I obtain are:
-3r + 48r + 24r
12s +29s + 56s
76t + 98t + 97t

You have not typed any equations. All equations contain an equals sign. When you post an equation, you must post both sides!

Also, this exercise asks for three parts ("express each column vector of AA…"), so work on them one at a time.

The first column of AA is:

-3
48
24

You need to obtain that column by combing scalar multiples of the columns of A.

    [3]         [-2]         [7]  =  [-3]
r * [6]  +  s * [ 5]  +  t * [4]  =  [48]
    [0]         [ 4]         [9]  =  [24]

Can you find r, s and t? You may be surprised at their values; there's a pattern in this exercise.

Set up linear combinations of r, s and t the same way, for the other two parts of the exercise (expressing the second and third columns of AA).

?