91Ó°ÊÓ

Let $$A=\left[\begin{array}{lll}1 & 2 & 3 \\\0 & 2 & 1 \\\3 & 1 & 0\end{array}\right]$$ Determine whether the matrix A has an inverse by finding whether the determinant is non zero. If the determinant is nonzero, find the inverse using the formula for the inverse which involves the cofactor matrix.

Find the determinants of the following matrices. (a) \(\left[\begin{array}{ll}1 & 3 \\ 0 & 2\end{array}\right]\) (b) \(\left[\begin{array}{ll}0 & 3 \\ 0 & 2\end{array}\right]\) (c) \(\left[\begin{array}{ll}4 & 3 \\ 6 & 2\end{array}\right]\)

Let \(A=\left[\begin{array}{rrr}1 & 2 & 4 \\ 0 & 1 & 3 \\ -2 & 5 & 1\end{array}\right]\). Find the following. (a) \(\operatorname{minor}(A)_{11}\) (b) \(\operatorname{minor}(A)_{21}\) (c) \(\operatorname{minor}(A)_{32}\) (d) \(\operatorname{cof}(A)_{11}\) (e) \(\operatorname{cof}(A)_{21}\) (f) \(\operatorname{cof}(A)_{32}\)

Let $$A=\left[\begin{array}{lll}1 & 2 & 0 \\\0 & 2 & 1 \\\3 & 1 & 1\end{array}\right]$$ Determine whether the matrix A has an inverse by finding whether the determinant is non zero. If the determinant is nonzero, find the inverse using the formula for the inverse.

Find the determinants of the following matrices. \((a)\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 2 & 2 \\ 0 & 9 & 8\end{array}\right]\) (b) \(\left[\begin{array}{rrr}4 & 3 & 2 \\ 1 & 7 & 8 \\ 3 & -9 & 3\end{array}\right]\) (c) \(\left[\begin{array}{llll}1 & 2 & 3 & 2 \\ 1 & 3 & 2 & 3 \\ 4 & 1 & 5 & 0 \\ 1 & 2 & 1 & 2\end{array}\right]\)

Let $$A=\left[\begin{array}{lll}1 & 3 & 3 \\\2 & 4 & 1 \\\0 & 1 & 1\end{array}\right]$$ Determine whether the matrix A has an inverse by finding whether the determinant is non zero. If the determinant is nonzero, find the inverse using the formula for the inverse.

Let $$A=\left[\begin{array}{lll}1 & 2 & 3 \\\0 & 2 & 1 \\\2 & 6 & 7\end{array}\right]$$ Determine whether the matrix \(A\) has an inverse by finding whether the determinant is non zero. If the determinant is nonzero, find the inverse using the formula for the inverse.

Find the following determinant by expanding along the first row and second column. $$\left|\begin{array}{lll}1 & 2 & 1 \\\2 & 1 & 3 \\\2 & 1 & 1\end{array}\right|$$

Let $$A=\left[\begin{array}{lll}1 & 0 & 3 \\\1 & 0 & 1 \\\3 & 1 & 0\end{array}\right]$$ Determine whether the matrix \(A\) has an inverse by finding whether the determinant is non zero. If the determinant is nonzero, find the inverse using the formula for the inverse.

Find the following determinant by expanding along the first column and third row. $$\left|\begin{array}{lll}1 & 2 & 1 \\\1 & 0 & 1 \\\2 & 1 & 1\end{array}\right|$$