15409600
| Question | Answer |
| What the determinant of a singular matrix? | |M| = 0 |
| Can we invert a singular matrix? | No |
| All reflections when inverted are.... | The same as reflections are self-inverse |
| A 30 degree rotation CW has the inverse... | 30 degree rotation AC |
| An enlargement of sf 3 centre (0,0) has the inverse.... | Enlargement sf 1/3 centre (0,0) |
| To find an unknown value in a singular matrix, e.g. [-2 4][1 p] , we use.... | The determinant (ad-bc=0 , so (-2)(p)-(4)(1)=0, -2p-4=0, 2p=-4, p=-2) |
| What is different when we find an unknown value in a non-singular matrix? | We use ≠ instead of = |
| What is the formula for finding an inverse matrix? (Lets say M=[a b][c d]) | M-1 = 1/ad-bc(d -b)(-c a) (for ad-bc≠0) |
| M x M-1 = .... and M-1 x M = .... | Identity Matrix (I) |
| B-1A-1 = .... | (AB)-1 |
| |A-1| = .... | 1/|A| (as |AB| = |A||B|) |
| For AX=B , if we have the matrices A and B, how would we find X? | AX=B , A-1 x A = B x A-1 (A x A-1 = I) , IX = B x A-1 (I x X = X), so : X=B x A-1 This method works for all rearrangements of X |
| What matrices represents the simultaneous equation 2x+3y =16 // -4x+y=3 ? | [2 3][-4 1] x [x][y] = [16][3] (x values on left , y values on right for first matrix) |
| If we know M[x][y] = [16][3] , how do we find the values of x and y? (if we know M) | Do MM-1[x][y] = [16][3]M-1, which is the same as [x][y] = [16][3]M-1 , and multiply together to get [x][y]. |
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