So i have an algebra problem that states "Using elementary row operations, show that the matrix is equal to 0".
I'm given this matrix and I don't know what they mean by this? Am I supposed to turn all of the elements into zeros, or only one row?
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10It is about determinant, not matrix. – zkutch Aug 12 '22 at 22:17
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Welcome to MSE. Do not use pictures of problem statements, see here for the reasons. – Thomas Preu Aug 12 '22 at 22:21
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@zkutch So how exactly am I supposed to prove that with elementary row operations? Which form of the matrix do I need to achieve? – tino Aug 12 '22 at 22:24
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You can find material on formatting math here. – Thomas Preu Aug 12 '22 at 22:25
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1@tino -- you need to show that the matrix is not invertible -- perhaps that you can get a row of zeros? – Annika Aug 12 '22 at 23:46
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As mentioned in the comments, you are being asked to show that the determinant of this matrix is zero. This can be shown if the rank of the matrix is $<3$.
You can do this by showing the rows are not linearly independent (hence the matrix is not invertible, and thus the determinant is $0$)
HINT: Focus on the first column, and try show that one of the rows equals some combination of the other two. Then check that the same relation holds for the other two columns.
Annika
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Hint:
If you add the top row to the bottom row, and then subtract two copies of the centre row from the bottom row, what do you get? And what is the determinant of a matrix of that type?
On notation:
Vertical straight bars on the left and right, like this: $$ \begin{vmatrix} a & b\\ c & d\\ \end{vmatrix} $$ means the determinant of the matrix. In the case of a $2\times2$ matrix that is $ad-bc$.
Suzu Hirose
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