- Matrix addition,
`A + B`

, subtraction,`A - B`

and multiplication,`A * B`

apply as follows:

**NB: according to matrix algebra, the order in which the matrices are placed during multiplication does matter i.e. it is expected that A*B would usually yield different results from B*A.**

- Matrix division is carried out using the
`/`

or`\`

where`B/A`

is equivalent to carrying out`B * inv(A)`

.`A\B`

on the other hand is the same as`inv(A) * B`

; this arrangement is especially useful when seeking to find the solution X to the equation AX = B (as in solving using Gaussian elimination). This would be further demonstrated in the exercise section.

**EXERCISE 4**

Using matrices A and B calculate;

(a) `F =A*B`

(b) `G = B*A`

(c) `H = F – G`

(d) `J = B’*A’`

(e) `K = F - J`

**MISCELLANEOUS EXERCISE**

Using MATLAB solve the following system of simultaneous equations:

3x + 2y – z = 10

-x + 3y + 2z = 5

x – y – z = -1

Hint: AX = B.

Solve this question using both the `\`

operator and inverse methods (see above). Is there any difference between both methods? Why is the inverse method not `B*inv(A)`

?