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{:[quad A=[[1,2,3],[4,5,6],[7,8,9]]quad B=[[2,4,6],[8,10,12],[14,16,18]]quad C=[[1,3,5],[7,9,11],[13,15,17]]],[2A-3B+4C]:}

A=[123456789]B=[24681012141618]C=[1357911131517]2A−3B+4C \begin{array}{l}\quad A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right] \quad B=\left[\begin{array}{ccc}2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18\end{array}\right] \quad C=\left[\begin{array}{ccc}1 & 3 & 5 \\ 7 & 9 & 11 \\ 13 & 15 & 17\end{array}\right] \\ 2 A-3 B+4 C\end{array}

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Full solution

Q. A=[123456789]B=[24681012141618]C=[1357911131517]2A−3B+4C \begin{array}{l}\quad A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right] \quad B=\left[\begin{array}{ccc}2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18\end{array}\right] \quad C=\left[\begin{array}{ccc}1 & 3 & 5 \\ 7 & 9 & 11 \\ 13 & 15 & 17\end{array}\right] \\ 2 A-3 B+4 C\end{array}
  1. Calculate 2A2A: First, let's calculate 2A2A.2A=2×[123 456 789]2A = 2 \times \left[\begin{array}{ccc}1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9\end{array}\right]=[2×12×22×3 2×42×52×6 2×72×82×9]= \left[\begin{array}{ccc}2\times 1 & 2\times 2 & 2\times 3 \ 2\times 4 & 2\times 5 & 2\times 6 \ 2\times 7 & 2\times 8 & 2\times 9\end{array}\right]=[246 81012 141618]= \left[\begin{array}{ccc}2 & 4 & 6 \ 8 & 10 & 12 \ 14 & 16 & 18\end{array}\right]
  2. Calculate 3B3B: Now, let's calculate 3B3B.
    3B=3×[246 81012 141618]3B = 3 \times \begin{bmatrix}2 & 4 & 6 \ 8 & 10 & 12 \ 14 & 16 & 18\end{bmatrix}
    3B=[3×23×43×6 3×83×103×12 3×143×163×18]\phantom{3B} = \begin{bmatrix}3\times2 & 3\times4 & 3\times6 \ 3\times8 & 3\times10 & 3\times12 \ 3\times14 & 3\times16 & 3\times18\end{bmatrix}
    3B=[61218 243036 424854]\phantom{3B} = \begin{bmatrix}6 & 12 & 18 \ 24 & 30 & 36 \ 42 & 48 & 54\end{bmatrix}
  3. Calculate 4C4C: Next, we calculate 4C4C.4C=4×[135 7911 131517]4C = 4 \times \left[\begin{array}{ccc}1 & 3 & 5 \ 7 & 9 & 11 \ 13 & 15 & 17\end{array}\right] =[4×14×34×5 4×74×94×11 4×134×154×17]= \left[\begin{array}{ccc}4\times 1 & 4\times 3 & 4\times 5 \ 4\times 7 & 4\times 9 & 4\times 11 \ 4\times 13 & 4\times 15 & 4\times 17\end{array}\right] =[41220 283644 526068]= \left[\begin{array}{ccc}4 & 12 & 20 \ 28 & 36 & 44 \ 52 & 60 & 68\end{array}\right]
  4. Add and Subtract Matrices: Now we add and subtract the matrices: 2A−3B+4C2A - 3B + 4C.
    \begin{bmatrix}2 & 4 & 6\8 & 10 & 12\14 & 16 & 18\end{bmatrix} - \begin{bmatrix}6 & 12 & 18\24 & 30 & 36\42 & 48 & 54\end{bmatrix} + \begin{bmatrix}4 & 12 & 20\28 & 36 & 44\52 & 60 & 68\end{bmatrix}
    =[(2−6+4)(4−12+12)(6−18+20)$8−24+28)(10−30+36)(12−36+44)$14−42+52)(16−48+60)(18−54+68)]= \begin{bmatrix}(2-6+4) & (4-12+12) & (6-18+20)\$8-24+28) & (10-30+36) & (12-36+44)\$14-42+52) & (16-48+60) & (18-54+68)\end{bmatrix}
    = \begin{bmatrix}0 & 4 & 8\12 & 16 & 20\24 & 28 & 32\end{bmatrix}

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