1.
\left(\begin{matrix}
4 & 1 \\
2 & 3
\end{matrix}\right)
= ?
Solution:
\\[3mm]
= (4 \times 3) - (2 \times 1) \\
= 12 - 2
2.
\left(\begin{matrix}
10 & 0 & -3 \\
-2 & -4 & -1 \\
3 & 0 & 2
\end{matrix}\right)
= ?
Solution:
\\[3mm]
10
\left(\begin{matrix}
5 + 1 \\
1 + 7
\end{matrix}\right)
-
(-2)
\left(\begin{matrix}
0 + -3 \\
0 + 2
\end{matrix}\right)
+
3
\left(\begin{matrix}
0 + -3 \\
-4 + 1
\end{matrix}\right)
\\[4mm]
= 10[(-4)(2) - (0)(1)] + 2[(0)(2) - (0)(-3)] + 3[(0)(1) - (-4)(-3)]
\\[4mm]
=10(−8)+2(0)+3(−12)
\\[4mm]
= −80 − 36
3.
\left(\begin{matrix}
4 & 1 & 7\\
2 & 3 & 5
\end{matrix}\right)
= ?
Answer:
this matrix is not square so it has no determinant
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