1 - Matrices

Question 1

matrix

Answer 1

an array of numbers
used to
- represent linear transformations
- solve linear simultaneous equations

Question 2

dimensions of a matrix

Answer 2

its size
rows then columns

Question 3

adding/ subtracting matrices

Answer 3

add together the corresponding elements of each matrix

Question 4

square matrix

Answer 4

same no. rows and columns

Question 5

zero matrix

Answer 5

all elements are zero

Question 6

identity matrix I

Answer 6

ones in the leading diagonal
100
010
001

Question 7

multiplying by I

Answer 7

AI = IA = A

Question 8

multiplying matrices

Answer 8

star with the first row and column and sum the products of each pair - repeat for next column - then repeat for all the rows
- dimensions have to agree eg 2 2 x 23 = 2*3

Question 9

raising to power

Answer 9

only square matrices

Question 10

determinant of a 2*2

Answer 10

a b
c d
det(A) = ad - bc
if = 0 then its singular (no inverse)
if != 0 then its non-singular (has inverse)

Question 11

inversing a 2*2

Answer 11

a b
c d
A-1 = 1/det(A) (d -b
-c a)
if Ax = y then A-1y = x
AA-1 = I

Question 12

determinant of a 3*3

Answer 12

a b c
d e f
g h I
det(A) = a(det(efhi) + b(det(fdig) + c(det(degh)

Question 13

minors matrix

Answer 13

for each element find the determinant of the 2*2 after the row and column with that element have been crossed out

Question 14

transposing a matrix

Answer 14

where the rows and columns are interchanged (rows become columns columns become rows)

Question 15

inversing a 3*3

Answer 15

• find det(A)
• find the minors matrix
• find matrix of co factors (+ - + etc)
• transpose

Question 16

using matrices to solve simultaneous eq

Answer 16

• put the LHS into a matrix * by the x, y, z matrix = put the RHS into a matrix
• and solve matrices

Question 17

consistency of linear eq

Answer 17

one point of intersection - consistent - 1 solution - non-singular matrix
parallel - inconsistent - no solutions - singular matrix
same line - consistent - infinite solutions - singular matrix

Question 18

consistency of 3 variable eq

Answer 18

planes meet at one point - consistent - 1 solution
sheaf - consistent - infinite solutions
prism - inconsistent
2 parallel one not - inconsistent
all the same - consistent - infinite solutions