Determinant of a Matrix

Find the determinants for the below matrices


1.

\left(\begin{matrix} 4 & 1 \\ 2 & 3 \end{matrix}\right) = ?

Solution:
\\[3mm] = (4 \times 3) - (2 \times 1) \\ = 12 - 2

Answer:
\\[3mm] 10


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

Answer:
\\[3mm] = -116


3.

\left(\begin{matrix} 4 & 1 & 7\\ 2 & 3 & 5 \end{matrix}\right) = ?

Solution:

no solution


Answer:

this matrix is not square so it has no determinant





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