# For what values of $k$ is matrix invertible

I want to know what value $k$ can not be for the matrix

A = {{4, 0, 2}, {-1, 2, 0}, {3, 1 , k}}


to have an inverse (be invertible).

I now you use the Inverse[A] to find the inverse but that is not the assignment.

• You are on the wrong site. This is for the Mathematica software package. You are looking for math.stackexchange.com – MarcoB May 23 '18 at 15:52
• No i want to use mathematica to solve for it – Fanny May 23 '18 at 15:55
• OK, then start by showing us your matrix in MMA notation, i.e. as a list of lists, and anything else that you have tried. Also, think of the mathematical condition for a matrix to be invertible... – MarcoB May 23 '18 at 15:57
• @MarcoB thank u I have updated – Fanny May 23 '18 at 16:00
• Thank you. So now, you probably know that a matrix is invertible iff its determinant is nonzero. So you could calculate the determinant symbolically (see Det), then use that expression to construct an equation to find the values for which the determinant is zero. You then solve the equation (e.g. using Solve, Reduce) to find k. – MarcoB May 23 '18 at 16:04

Having defined

A = {{4, 0, 2}, {-1, 2, 0}, {3, 1 , k}}


then

Solve[Det[A] == 0, k]


yields

 {{k -> 7/4}}

• I get $7/4$ rather than your value. Are you using the matrix in the OP? – MarcoB May 23 '18 at 16:08
• maybe i mistyped a number... – xin pei May 24 '18 at 6:16