Arithmetic Operators 2

  • 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.

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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


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)?