FP 1 Matrices Introduction BAT multiply matrices Matrix
FP 1 Matrices Introduction BAT multiply matrices
Matrix multiplication These numbers will give the dimensions of the answer These numbers must be the same for the multiplication to be possible You multiply each row in the first matrix, by each column in the second matrix The product will have the same number of rows as the first matrix, and the same number of columns as the second
Dimensions for AB (2 x 2) x (2 x 1) = (2 x 1) à To multiply matrices you first multiply corresponding elements of the rows and columns, then add them up (you’ll get it with practice!) à Then once you have done all the columns, do the same thing, but using the second row… à After this, work out each part, and you then have the final matrix answer! Dimensions for BA (2 x 1) x (2 x 2) = not possible
Calculating AB Dimensions for AB (2 x 2) x (2 x 2) = (2 x 2) àMultiply the first row by each column as in the previous example àYou always fill in the top row of the answer first à A quick check – you have probably done this correctly if the highlighted (green) numbers are the same!
Calculating BA Dimensions for BA (2 x 2) x (2 x 2) = (2 x 2) àMultiply the first row by each column as in the previous example àYou always fill in the top row of the answer first à A quick check – you have probably done this correctly if the highlighted (green) numbers are the same!
AB = dimensions (1 x 3) x (1 x 2) not possible As the central numbers are not equal, these matrices cannot be combined
Calculating BCA This can be done in one of two ways 1) (BC)A Multiply B by C, and the answer to that by A (in that order) 2) B(CA) Multiply C by A, and multiply B by the answer to that (in that order) Remember you cannot change the order, so for method 2, do not do CA and then x B after, the B must go at the front!
Matrices - multiplying Find (where possible): i) AB ii) BA v) DA vi) AD iii) BC vii) CD To multiply matrices what must be true? iv) CB viii) DC
Matrices - multiplying Find (where possible): v) DA vi) AD vii) CD viii) DC To multiply matrices what must be true?
Matrices - multiplying Find (where possible): v) DA vi) AD vii) CD viii) DC To multiply matrices what must be true?
As BA = 0, the implication is that –b + 2 a = 0 We know from before that 2 a = b so we can replace the b terms…
Summary Crucial points: Make sure that you can do matrix multiplication confidently Remember that matrix multiplication is NOT commutative AB BA
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