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Opérations sur les matrices : Addition et soustraction - Exercice 4

12 min

{\color{red}\underline{COMPETENCE}\;:\;Calculer}

On considère les matrices suivantes :

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

B=\left(\begin{array}{cc} {5} & {6} \\ {2} & {-5} \end{array}\right)

Question 1

Calculer : $A+B$

Correction

A+B=\left(\begin{array}{cc} {\red{-2}} & {\blue{3}} \\ {\green{4}} & {\pink{1}} \end{array}\right)+\left(\begin{array}{cc} {\red{5}} & {\blue{6}} \\ {\green{2}} & {\pink{-5}} \end{array}\right)

A+B=\left(\begin{array}{cc} {\red{-2}+\red{5}} & {\blue{3}+\blue{6}} \\ {\green{4}+\green{2}} & {\pink{1}+\left(\pink{-5}\right)} \end{array}\right)

A+B=\left(\begin{array}{cc} {3} & {9} \\ {6} & {-4} \end{array}\right)

Question 2

Correction

A-B=\left(\begin{array}{cc} {\red{-2}} & {\blue{3}} \\ {\green{4}} & {\pink{1}} \end{array}\right)-\left(\begin{array}{cc} {\red{5}} & {\blue{6}} \\ {\green{2}} & {\pink{-5}} \end{array}\right)

A-B=\left(\begin{array}{cc} {\red{-2}-\red{5}} & {\blue{3}-\blue{6}} \\ {\green{4}-\green{2}} & {\pink{1}-\left(\pink{-5}\right)} \end{array}\right)

A-B=\left(\begin{array}{cc} {-7} & {-3} \\ {2} & {6} \end{array}\right)

Question 3

Correction

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

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

\purple{3}A=\left(\begin{array}{cc} {-6} & {9} \\ {12} & {3} \end{array}\right)

Question 4

Correction

{\color{blue}{4}}B={\color{blue}{4}}\times\left(\begin{array}{cc} {5} & {6} \\ {2} & {-5} \end{array}\right)

{\color{blue}{4}}B=\left(\begin{array}{cc} {5\times\color{blue}{4}} & {6\times\color{blue}{4}} \\ {2\times\color{blue}{4}} & {-5\times\color{blue}{4}} \end{array}\right)

{\color{blue}{4}}B=\left(\begin{array}{cc} {20} & {24} \\ {8} & {-20} \end{array}\right)

Question 5

Correction

D'après les questions précédentes, nous savons que :

3A=\left(\begin{array}{cc} {-6} & {9} \\ {12} & {3} \end{array}\right)

4B=\left(\begin{array}{cc} {20} & {24} \\ {8} & {-20} \end{array}\right)

On a :

3A-4B=\left(\begin{array}{cc} {\red{-6}} & {\blue{9}} \\ {\green{12}} & {\pink{3}} \end{array}\right)-\left(\begin{array}{cc} {\red{20}} & {\blue{24}} \\ {\green{8}} & {\pink{-20}} \end{array}\right)

3A-4B=\left(\begin{array}{cc} {\red{-6}-\red{20}} & {\blue{9}-\blue{24}} \\ {\green{12}-\green{8}} & {\pink{3}-\left(\pink{-20}\right)} \end{array}\right)

3A-4B=\left(\begin{array}{cc} {-26} & {-15} \\ {4} & {23} \end{array}\right)

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