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