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Given
L=[[4,1],[3,-2]]quad M=[[3,0],[0,1]] and
N=[[2,3],[4,1]]

Evaluate i.
2N-L
ii.
(NM)L

Given $\newline$ $L=[[4,1],[3,-2]]$ $\quad$ $M=[[3,0],[0,1]]$ and $\newline$ $N=[[2,3],[4,1]]$ $\newline$ Evaluate i. $\newline$ $2N-L$ $\newline$ ii. $\newline$ $(NM)L$

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Unions and intersections of sets

Full solution

Q. Given

\newline

L=[[4,1],[3,-2]]

\quad

M=[[3,0],[0,1]]

and

\newline

N=[[2,3],[4,1]]

\newline

Evaluate i.

\newline

2N-L

\newline

ii.

\newline

(NM)L

Identify matrices $L$ , $M$ , and $N$ : Identify matrices $L$ , $M$ , and $N$ . $L = \left[\begin{array}{cc}4 & 1 \ 3 & -2\end{array}\right]$ , $M = \left[\begin{array}{cc}3 & 0 \ 0 & 1\end{array}\right]$ , $N = \left[\begin{array}{cc}2 & 3 \ 4 & 1\end{array}\right]$
Calculate $2N$ : Calculate $2N$ . $2N = 2 \times \left[\begin{array}{cc}2 & 3 \ 4 & 1\end{array}\right] = \left[\begin{array}{cc}4 & 6 \ 8 & 2\end{array}\right]$
Perform $2N - L$ : Perform $2N - L$ .2N - L = \left[\begin{array}{cc}4 & 6\8 & 2\end{array}\right] - \left[\begin{array}{cc}4 & 1\3 & -2\end{array}\right] = \left[\begin{array}{cc}0 & 5\5 & 4\end{array}\right]
Calculate NM: Calculate NM ( $N$ multiplied by $M$ ). $\newline$ $NM = [[2\times3 + 3\times0, 2\times0 + 3\times1], [4\times3 + 1\times0, 4\times0 + 1\times1]] = [[6, 3], [12, 1]]$
Perform $(NM)L$ : Perform $(NM)L$ $(NM$ multiplied by $L)$ . $(NM)L = \left[\begin{array}{cc}6 & 3 \ 12 & 1\end{array}\right] * \left[\begin{array}{cc}4 & 1 \ 3 & -2\end{array}\right] = \left[\begin{array}{cc}6\cdot4 + 3\cdot3 & 6\cdot1 + 3\cdot(-2) \ 12\cdot4 + 1\cdot3 & 12\cdot1 + 1\cdot(-2)\end{array}\right]$ = \left[\begin{array}{cc} $33$ & $0$ \ $51$ & $10$ \end{array}\right]

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