Answer to Question #234347 in Algebra for Carlito

Question #234347

determine values of y if the matrix has no inverse


{2y2 2}


{1 0}


1
Expert's answer
2021-09-08T06:43:02-0400

A matrix has no inverse if and only if its determinant is 0.


detA=2y2210=20,yR\det A=\begin{vmatrix} 2y^2 & 2\\ 1 & 0 \end{vmatrix}=-2\not=0, y\in \R

The matrix (2y2210)\begin{pmatrix} 2y^2 & 2 \\ 1 & 0 \end{pmatrix} has inverse for yR.y\in \R.

Therefore there are no values of yy for which the matrix (2y2210)\begin{pmatrix} 2y^2 & 2 \\ 1 & 0 \end{pmatrix} has no inverse.


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