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Soient les matrices suivantes : $A = \begin{pmatrix} -1 & 0 \ 3 & 2 \end{pmatrix}$ ; $B = \begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}$ ; $C= \begin{pmatrix} 1 & 0 \ 2 & 4 \ 0 & -3 \end{pmatrix}$ calcule $3B – 2 C$

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Transformations of functions

Full solution

Q. Soient les matrices suivantes :

A = \begin{pmatrix} -1 & 0 \ 3 & 2 \end{pmatrix}

;

B = \begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}

;

C= \begin{pmatrix} 1 & 0 \ 2 & 4 \ 0 & -3 \end{pmatrix}

calcule

3B – 2 C

Multiply Matrix B by $3$ : Step $1$ : Multiply matrix B by $3$ . $\newline$ Matrix B = $\begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}$ $\newline$ $3B = 3 \times \begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}$ $\newline$ = $\begin{pmatrix} 12 & -9 \ 0 & 6 \ 3 & 0 \end{pmatrix}$
Multiply Matrix C by $2$ : Step $2$ : Multiply matrix C by $2$ . $\newline$ Matrix C = $\begin{pmatrix} 1 & 0 \ 2 & 4 \ 0 & -3 \end{pmatrix}$ $\newline$ $2C = 2 \times \begin{pmatrix} 1 & 0 \ 2 & 4 \ 0 & -3 \end{pmatrix}$ $\newline$ = $\begin{pmatrix} 2 & 0 \ 4 & 8 \ 0 & -6 \end{pmatrix}$
Subtract $2$ C from $3$ B: Step $3$ : Subtract $2C$ from $3B$ . $3B - 2C = \left| \begin{array}{cc} 12 -9 \ 0 6 \ 3 0 \end{array} \right| - \left| \begin{array}{cc} 2 0 \ 4 8 \ 0 -6 \end{array} \right|$ $= \left| \begin{array}{cc} 12-2 -9-0 \ 0-4 6-8 \ 3-0 0+6 \end{array} \right|$ $= \left| \begin{array}{cc} 10 -9 \ -4 -2 \ 3 6 \end{array} \right|$

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