Question

For the determinant $\left[\begin{array}{ccc}1& -1& 4\\ 0& 2& -1\\ -2& -3& 3\end{array}\right]$, find and then evaluate the minor of (a) a₁ (b) b₂ (c) c₃

Short answer

The minor of a₁=3

The minor of b₂=11

The minor of c₃=2

Step-by-step solution

Step 1. Given information

The given determinant is

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

Step 2. Calculation

(a) Eliminate the row and column that contains a1.

and write 2*2 determinant that remains

$$\begin{gathered} \mathrm{minor}\mathrm{of}{a}_1=\left|\begin{array}{cc}2& -1\\ -3& 3\end{array}\right| \\ \mathrm{by}\mathrm{evaluating}=(3\times 2)-(-1\times -3) \\ =6-3 \\ =3 \end{gathered}$$

(b) Eliminate the row and column that contains b2.

and write 2*2 determinant that remains

$$\begin{gathered} \mathrm{minor}\mathrm{of}{b}_2=\left|\begin{array}{cc}1& 4\\ -2& 3\end{array}\right| \\ \mathrm{by}\mathrm{evaluating}=(3\times 1)-(4\times -2) \\ =3-(-8) \\ =3+8 \\ =11 \end{gathered}$$

(c) Eliminate the row and column that contains c3.

and write 2*2 determinant that remains

$$\begin{gathered} \mathrm{minor}\mathrm{of}{c}_3=\left|\begin{array}{cc}1& -1\\ 0& 2\end{array}\right| \\ \mathrm{by}\mathrm{evaluating}=(2\times 1)-(-1\times 0) \\ =2-0 \\ =2 \end{gathered}$$