for what value of a,
$\begin{bmatrix}2a & -1\\-8 & 3\end{bmatrix}$
is a singular matrix. Can you also explain to me how to prove that a matrix is a singular matrix?
What should be the value of a for it to be a singular matrix
3
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matrices
2 Answers
3
A matrix is singular if it has a $0$ determinant. In your case, the determinant is $2a \cdot 3 - (-1)(-8) = 6a - 8$ so the determinant is $0$ precisely when $6a - 8 =0 \iff a = \frac{4}{3}$.
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0Let M be a nxn matrix, M is singular iff det(M) = 0 – 2017-02-25
1
A matrix is singular iff a linear combination of its rows or columns is a null vector.
In you example take $k$ times the first row and add the second:$$ k(2a,-1)+(-8, 3)=(2ka-8,-k+3)$$ To null the second component we have $k=3$, then to null the first component $6a=8$