Matrices Flashcards
What is the rule for matrix multiplication?
The columns of matrix A = the rows of matrix B (i.e. if matrix A = 2 x 3, and matrix B = 3 x 4, then you can multiply because the inside numbers are equal (the 3))
What are the dimension of a 2 x 4 and a 4 x 6 matrix multiplied together
2 x 6 (remove the common number)
Can you multiply a 4 x 4 and a 5 x 4 matrix?
No, the columns of A do not equal the rows of B
How do you find the determinant of a 2 x 2 matrix? (e.g. a b )
c d
You multiply the leading diagonal, and minus is by the non-leading diagonal multiplied. ad - bc
How do you find the inverse of a 2 x 2 matrix?
1/ determinant x (d -b)
-c a
What does A^-1 x A equal?
The Identity matrix
When a question asks you to find the characteristic polynomial, what do you need to find?
The eigenvalues and eigenvectors
What’s the formula to find the eigenvalues?
det(M-‘lamda’I) = 0
where:
det = determinant
M = matrix
‘lamda’ = the lamda greek letter
I = the Identity matrix
What is the formula to find the eigenvectors?
Mv = ‘lamda’v
What is the formula for diagonalisation?
M = PDP^1
where:
M = matrix
P = your eigenvectors put together in a matrix form
D = your eigenvalues in a diagonal matrix
What operation do you use for reflection/ rotation and enlargement?
Multiplication
What operation do you use for translation?
Addition
