Question

Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.

Answer 1

Answer:

This shows 3 pivot position matrixes.

Step-by-step explanation:

The given matrix is:  

$\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-3&3&0\end{array}\right]$

The option D is correct for this matrix.

The matrix is invertible and the given matrix has 3 pivot positions.

The matrix is invertible if its determinant is nonzero.

Multiply the 3rd row by 1/3.we get:

$\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-1&1&0\end{array}\right]$

Now, add the first row with third row:

$\left[\begin{array}{ccc}0&-1&-5\\0&4&3\\-1&1&0\end{array}\right]$

Replace third row by first row:

$\left[\begin{array}{ccc}-1&1&0\\0&4&3\\0&-1&-5\end{array}\right]$

This shows 3 pivot position matrixes.

Hence, a matrix is invertible and has 3 pivot positions.