Karteikarten
Inverse Matrices
Karten in diesem Stapel (14)
- 1What the determinant of a singular matrix?|M| = 0
- 2Can we invert a singular matrix?No
- 3All reflections when inverted are....The same as reflections are self-inverse
- 4A 30 degree rotation CW has the inverse...30 degree rotation AC
- 5An enlargement of sf 3 centre (0,0) has the inverse....Enlargement sf 1/3 centre (0,0)
- 6To 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)
- 7What is different when we find an unknown value in a non-singular matrix?We use ≠ instead of =
- 8What 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) - 9M x M-1 = .... and M-1 x M = ....Identity Matrix (I)
- 10B-1A-1 = ....(AB)-1
- 11|A-1| = ....1/|A|
(as |AB| = |A||B|) - 12For 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 - 13What 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) - 14If 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].