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In general if $A$ is an $m \\times n$ matrix with typical element $a_{ij}$ then the product of a number $k$ with $A$ is written $kA$ and has the corresponding elements $ka_{ij}$ .

If $ A= \\left( \\begin{array}{ccc} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\\\ a_{31} & a_{32} \\end{array} \\right) $ then $ kA= \\left( \\begin{array}{ccc} k \\times a_{11} & k \\times a_{12} \\\\ k\\times a_{21} &k\\times a_{22} \\\\ k\\times a_{31} &k\\times a_{32} \\end{array} \\right) $

This operation is called scalar multiplication, but its result is not named \"scalar product\" to avoid confusion, since \"scalar product\" is often used as a synonym for the \"dot product\" or \"inner product\".

", "advice": "

We are asked to carry out scalar multiplications of the given matrices.

This is simply achieved by multiplying each element by the constant:

Using this technique results in:

If $A=\\var{A}$ then: $\\var{k1} A=\\left( \\begin{array}{ccc} \\var{k1} \\times \\var{A[0][0]} & \\var{k1} \\times \\var{A[0][1]}& \\var{k1} \\times \\var{A[0][2]}\\\\ \\var{k1} \\times \\var{A[1][0]} & \\var{k1} \\times \\var{A[1][1]}& \\var{k1} \\times \\var{A[1][2]}\\\\ \\var{k1} \\times \\var{A[2][0]} & \\var{k1} \\times \\var{A[2][1]} & \\var{k1} \\times \\var{A[2][2]} \\end{array} \\right) = \\var{ad1}$

Following the same process gives:

If $B=\\var{B}$ then:

$\\var{k2}B=\\var{ad2}$

If $C=\\var{C}$ then:

$\\var{k3}C=\\var{ad3}$

If $D=\\var{D}$ then:

$\\var{k4}D=\\var{ad4}$

If $E=\\var{EE}$ then:

$\\var{k5}E=\\var{ad5}$

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Carry out the scalar multiplication of the following matrices:

You will need to define the size of the matrix before entering your answer.

If $A=\\var{A}$ then:

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

If $B=\\var{B}$ then:

$\\var{k2}B=$ [[1]]

If $C=\\var{C}$ then:

$\\var{k3}C=$ [[2]]

If $D=\\var{D}$ then:

$\\var{k4}D=$ [[3]]

If $E=\\var{EE}$ then:

$\\var{k5}E=$ [[4]]

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