Is there any algorithm to determine whether a matrix is a linear combination of another set of matrices? For example, I want to find whether the matrix [1 0] can be written as a linear combination of the matrices [1 2] and [1 1].
Determine whether a matrix is a linear combination of a given set of matrices
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linear-algebra
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0I think I'll need to represent the linear combination of these matrices as a system of linear equations, and then convert the system of equations to row echelon form - how can I write this problem as a system of linear equations? – 2012-12-04
1 Answers
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Solve the system of equations $\begin{pmatrix} a+b \\ 2a +b \end{pmatrix}=\begin{pmatrix} 1 \\ 0 \end{pmatrix}$. If there is a solution, then it can be written as a linear combination. If there is no solution, then it can't be.
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1$xa_{ij}$ is $x$ times the $i,j$ entry of $A$. $ya_{ij}$ is defined similarly. – 2012-12-11