4 Multiplication of a matrix by a number

There is also a natural way of defining the product of a matrix with a number. Using the matrix [maths rendering] above, we note that

[maths rendering]

What we see is that [maths rendering] (which is the shorthand notation for [maths rendering] ) is obtained by multiplying every element of [maths rendering] by [maths rendering] .

In general if [maths rendering] is an [maths rendering] matrix with typical element [maths rendering] then the product of a number [maths rendering] with [maths rendering] is written [maths rendering] and has the corresponding elements [maths rendering] .

Hence, again using the matrix [maths rendering] above,

[maths rendering]

Similarly:

[maths rendering]

Task!

For the following matrices find, where possible, [maths rendering] .

  1. [maths rendering]
  2. [maths rendering]
  3. [maths rendering]
  1. [maths rendering] [maths rendering]
  2. [maths rendering] [maths rendering]

    [maths rendering]

  3. None of [maths rendering] are defined. [maths rendering]