# Thread: Matrix problem

1. ## Matrix problem

I don't even know where to start with this problem, I really don't understand it at all.

Could anyone help me please?

Problem:

Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible

2. ## Re: Matrix problem

Originally Posted by alexdudek
I don't even know where to start with this problem, I really don't understand it at all.

Could anyone help me please?

Problem:

Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
Hello,
$\left[ \begin{matrix}1 &2\\3&2 \end{matrix}\right]-\left[ \begin{matrix}0&1\\1&0\end{matrix}\right]=\left[ \begin{matrix}1&1\\2&2\end {matrix}\right]$ The resultant matrix is not invertible.

3. ## Re: Matrix problem

Originally Posted by alexdudek
I don't even know where to start with this problem, I really don't understand it at all.

Could anyone help me please?

Problem:

Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
An invertible 2x2 matrix has no inverse ie determinant is 0.

sI(subscript 2) is s times the 2x2 identity matrix, ie leading diagonal has elements s and others are 0.

So find A - sI, find an expression for the determinant, let it equal 0 and solve. (You should end up with a quadratic equation which will yield 2 solutions.) Give it a go.

4. ## Re: Matrix problem

Originally Posted by Vinod
Hello,
$\left[ \begin{matrix}1 &2\\3&2 \end{matrix}\right]-\left[ \begin{matrix}0&1\\1&0\end{matrix}\right]=\left[ \begin{matrix}1&1\\2&2\end {matrix}\right]$ The resultant matrix is not invertible.

5. ## Re: Matrix problem

Originally Posted by Debsta
Hello,
Sorry for providing irrelevant answer.
$\left[ \begin{matrix} 1&2\\3&2 \end{matrix} \right]$-$\left[ \begin {matrix}-1&0\\0&-1 \end {matrix}\right]$=$\left[ \begin{matrix}2&2\\ 3&3 \end{matrix} \right]$. The resultant matrix is not invertible.

6. ## Re: Matrix problem

Originally Posted by alexdudek
I don't even know where to start with this problem, I really don't understand it at all.

Could anyone help me please?

Problem:

Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
It is sad that you would be working with matrices and not know that "a matrix is invertible if and only if its determinant is non-zero". So you are looking for s such that $\displaystyle \left|\begin{bmatrix} 1 & 2 \\ 3 & 2\end{bmatrix}- s\begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix}\right|= \left |\begin{array}{cc}1- s & 2 \\ 3 & 2- a\end{array}\right|= (1- s)(2- s)- 6\ne 0$.

The matrix will NOT be invertible when $\displaystyle (1- s)(2- s)- 6= s^2- 3s- 4= 0$. Solve that quadratic equation.

7. ## Re: Matrix problem

Originally Posted by Debsta
A non- invertible 2x2 matrix has no inverse ie determinant is 0.

sI(subscript 2) is s times the 2x2 identity matrix, ie leading diagonal has elements s and others are 0.

So find A - sI, find an expression for the determinant, let it equal 0 and solve. (You should end up with a quadratic equation which will yield 2 solutions.) Give it a go.
(Edit... sorry)