- #1
MathNoob22
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Homework Statement
Let A be a 2x3 matrix with real coefficients, and suppose that neither of the two rows of A is a scalar multiple of the other. By quoting an appropriate theorem from linear algebra, show that for some j [tex]\in[/tex] {1,2,3}, the 2x2 matrix obtained by omitting the jth column of A is invertible
Homework Equations
Not really any necessary equations that I can think of. Only one I suppose is:
AA[tex]^{-1}[/tex] = I
So A has to be a square matrix in order for it to be invertible.
The Attempt at a Solution
I know in order for a matrix to be invertible, it has to be an nxn matrix. Also, the determinant of A cannot be equal to 0. So, if the rows are not multiples of each other, does that automatically mean that any 2x2 submatrix of A have a determinant not equal to 0?
Any help would be appreciated!