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

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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}

Calculer

3B – 2C

Multiply by $3$ : First, we need to multiply each element of matrix $B$ by $3$ . $B = \left| \begin{array}{cc} 4 & -3 \ 0 & 2 \ 1 & 0 \end{array} \right|$ $3B = \left| \begin{array}{cc} 3\times 4 & 3\times (-3) \ 3\times 0 & 3\times 2 \ 3\times 1 & 3\times 0 \end{array} \right|$ $= \left| \begin{array}{cc} 12 & -9 \ 0 & 6 \ 3 & 0 \end{array} \right|$
Multiply by $2$ : Next, multiply each element of matrix $C$ by $2$ . $C = \begin{pmatrix} 1 & 0 \ 2 & 4 \ 0 & -3 \end{pmatrix}$ $2C = \begin{pmatrix} 2\times 1 & 2\times 0 \ 2\times 2 & 2\times 4 \ 2\times 0 & 2\times (-3) \end{pmatrix}$ $= \begin{pmatrix} 2 & 0 \ 4 & 8 \ 0 & -6 \end{pmatrix}$
Subtract $2C$ from $3B$ : Now, subtract $2C$ from $3B$ . We need to subtract corresponding elements. $3B - 2C = \left| \begin{array}{cc} 12-2 & -9-0 \ 0-4 & 6-8 \ 3-0 & 0-(-6) \end{array} \right|$ = \left| \begin{array}{cc} $10$ & $-9$ \ $-4$ & $-2$ \ $3$ & $6$ \end{array} \right|

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