Matrices

Question 1

Scalar multiplication

Answer 1

multiply each element by scalar

Question 2

addition, subtraction

Answer 2

add, subtract elements in same position. Matrices must be equal size

Question 3

Multiplication

Answer 3

rows by columns. R1xC1 R1Xc2, underneath is R2xc1, R2xc2, etc

Question 4

Not commutative

Answer 4

AB not = BA

Question 5

To see if can be multiplied

Answer 5

write sizes of both, inside numbers must match, outside numbers size of new matrix 3x2 2x3 so new matrix will be 3 x 3

Question 6

Matrix powers

Answer 6

A^ is AA, A^3 is A^2A, A^6 is A^3A^3

Question 7

Network matrices

Answer 7

Input vector x Matrix representing network = output vector. No of columns = no of inputs, no of rows = no of outputs

Question 8

Identity matrix

Answer 8

Multiplying by it leaves original matrix unchanged. Square matrix. Diagonal set of “1” from top left to bottom right, all other elements 0

Question 9

Inverse of 2x2 matrix

Answer 9

top row a b, 2nd row cd. Determinant ad-bc, if not 0 then matrix invertible. Swap a and c elements, change sign on b and d ones, 1/det in front of matrix

Question 10

Solve simul eq with matrices

Answer 10

Rewrite eq so x + y (in same order) = constant. If no x or y, then 0x or 0y. That is the coefficient matrix. That by vector (x/y) = vector (constant/constant). Find inverse of coefficient matrix including 1/determinant (A^-1). So vector (x/y) A^-1 x vector (constant/constant)

Question 11

Simultaneous linear eq matrix coefficient determinant

Answer 11

if det is 0 then no or infinitely many solutions. If not 0 then unique solution