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Jika
A=([4,2],[-1,3]),B=([2,-1],[1,3]), dan matriks
C memenuhi
C=AB, nilai
det C=
A. 8
D. 18
B. 12
E. 22
C. 15

Jika $A=\left(\begin{array}{cc}4 & 2 \\ -1 & 3\end{array}\right), B=\left(\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right)$ , dan matriks $C$ memenuhi $C=A B$ , nilai $\operatorname{det} C=$ $\newline$ A. $8$ $\newline$ D. $18$ $\newline$ B. $12$ $\newline$ E. $22$ $\newline$ C. $15$

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Transformations of quadratic functions

Full solution

Q. Jika

A=\left(\begin{array}{cc}4 & 2 \\ -1 & 3\end{array}\right), B=\left(\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right)

, dan matriks

C

memenuhi

C=A B

, nilai

\operatorname{det} C=

\newline

A.

8

\newline

D.

18

\newline

B.

12

\newline

E.

22

\newline

C.

15

Calculate Matrix Product: Calculate the product of matrices $A$ and $B$ to find matrix $C$ .C = AB = \left(\begin{array}{cc}\(4 & $2$ (-1\) & $3$ \end{array}\right) * \left(\begin{array}{cc} $2$ & $-1$ (1\) & $3$ \end{array}\right) = \left(\begin{array}{cc} $4$ \times $2$ + $2$ \times $1$ & $4$ \times ( $-1$ )+ $2$ \times $3$ (-1\)\times $2$ + $3$ \times $1$ & $-1$ \times ( $-1$ )+ $3$ \times $3$ \end{array}\right) = \left(\begin{array}{cc} $8$ + $2$ & $-4$ + $6$ (-2\)+ $3$ & $1$ + $9$ \end{array}\right) = \left(\begin{array}{cc} $10$ & $2$ (1\) & $10$ \end{array}\right)
Find Determinant of Matrix C: Now, find the determinant of matrix C. $\text{det } C = (10)(10) - (2)(1)$ $= 100 - 2$ $= 98$

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