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Matrix calculations can often include a combination of operations such as addition, subtraction and scalar multiplication.

", "advice": "

We are asked to carry out combinations of matrix operations:

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If     $A=\\var{A}$          and     $B=\\var{A2}$     then:

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$\\var{k1} A+B=\\var{k1} \\var{A}+\\var{A2}$

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$\\var{k1} A+B=\\var{ad1}+\\var{A2}$

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$\\var{k1} A+B=\\var{ad1a}$

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If     $C=\\var{B}$          and     $D=\\var{B2}$     then:

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$C-\\var{k2}D=\\var{B}-\\var{k2}\\var{B2}$

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$C-\\var{k2}D=\\var{B}-\\var{ad2}$

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$C-\\var{k2}D=\\var{ad2a}$

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If     $E=\\var{C}$     and     $F=\\var{C2}$    then:

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$\\var{k3}E-\\var{k1}F=\\var{k3}\\var{C}-\\var{k1}\\var{C2}$

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$\\var{k3}E-\\var{k1}F=\\var{ad3}-\\var{ad3a}$

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$\\var{k3}E-\\var{k1}F=\\var{ad3b}$

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If     $G=\\var{D}$     and     $H=\\var{D2}$     then:

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$\\var{k4}G+H=\\var{k4}\\var{D}+\\var{D2}$

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$\\var{k4}G+H=\\var{ad4}+\\var{D2}$

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$\\var{k4}G+H=\\var{ad4a}$

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If     $I=\\var{EE}$     and     $J=\\var{EE2}$     then:

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$\\var{k5}I-J=\\var{k5}\\var{EE}-\\var{EE2}$

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$\\var{k5}I-J=\\var{ad5}-\\var{EE2}$

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$\\var{k5}I-J=\\var{ad5a}$

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Carry out the following matrix calculations:

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If     $A=\\var{A}$          and     $B=\\var{A2}$     then:

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$\\var{k1} A+B=$ [[0]]

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If     $C=\\var{B}$          and     $D=\\var{B2}$     then:

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$C-\\var{k2}D=$ [[1]]

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If     $E=\\var{C}$     and     $F=\\var{C2}$    then:

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$\\var{k3}E-\\var{k1}F=$ [[2]]

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If     $G=\\var{D}$     and     $H=\\var{D2}$     then:

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$\\var{k4}G+H=$ [[3]]

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If     $I=\\var{EE}$     and     $J=\\var{EE2}$     then:

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$\\var{k5}I-J=$ [[4]]

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