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Matrices for Linear Combination Vectors

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Determine if b is a linear combination of the vectors formed from the columns of the matrix A.

A = 1 -4 2 , b = 3
0 3 5 -7
-2 8 -4 -3

2) List 5 vectors in span (v1, v2). For each vector show the weights on v1 and v2 used to generate the vector and list the three entries of the vector. Do not make a sketch.

v1 = 7 , v2 = -5
1 3
-6 0

3) Give the geometric description of span (v1,v2) for the vectors.

u = 2 and v = 2
-1 1

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Solution Summary

The matrices for linear combination vectors are examined.

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Determine if b is a linear combination of the vectors formed from the columns of the matrix A.

A = , b =
If b is a linear combination of columns of matrix A, then
= a +b +c
Or
a - 4b + 2c = 3
0a + ...

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