Week 8 Linear Algebra 1

Question 1

what is the compact vector form for the matrix of two separate equations of x and y

Answer 1

Ax = v

Question 2

what is the 2x2 identity matrix in column vector form

Answer 2

1 0

0 1

Question 3

what is the general form for stretching a 2x2 matrix in column vector form

Answer 3

k 0

0 k

Question 4

what is the general form for reflecting a 2x2 matrix in column vector form

Answer 4

1 0

0 -1

Question 5

what is the general form for rotating a 2x2 matrix about an angle θ in column vector form

Answer 5

cos θ -sinθ

sin θ cosθ

Question 6

what is the condition in order for two matrices to be equal

Answer 6

all their matrix elements must be equal

Question 7

how do you add two matrices

Answer 7

add all of their elements that are in the same relative position together
eg
1 2 4 3 5 5
3 4 + 2 1 = 5 5

Question 8

what is the rule for multiplying a matrix by a scalar

Answer 8

multiply all of the terms by the scalar

Question 9

what is the rule for multiplying two matrices in the form of A x B

Answer 9

the number of columns in A = the number of rows in B otherwise it is not possible

Question 10

define the transpose of a matrix A

Answer 10

it is the matrix obtained by swapping the rows and columns of A

Question 11

give the equation that defines the inverse of a matrix

Answer 11

AA^-1 = Identity matrix

Question 12

what is the main condition that means that a matrix can’t have an inverse

Answer 12

the determinant of the matrix = 0

Question 13

what are the two possible outcomes if Ax = v has no unique solutions

Answer 13

1 the equation is inconsistent so you have straight parallel lines
2 the equation is degenerate so you have one equation that is a multiple of the other

Question 14

what is the equation for the inverse of a 3x3 matrix A

Answer 14

A^-1 = 1/detA x transpose of C

C is the matrix of cofactors