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

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-11-05

Determine if b is a linear combination of the vectors formed from the columns of the matrix A.
A=[142035284],b=[373]

Answer & Explanation

berggansS

berggansS

Skilled2021-11-06Added 91 answers

Step 1
We must ascertain if
b=[373]
is a linear combination of the vectors obtained from the A matrix's columns.
[A | b]=[142|3035|7284|3]
[142|3035|7284|3]R1R2R3+12R1R3[284|3035|7000|32]
The third formula is 0=32, Therefore, we draw the conclusion that the system cannot be solved.
The vectors created from the columns of matrix A are therefore not linearly combined to form b.
Result:
The vectors created from the columns of the matrix A are not linearly combined to yield the vector b.

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