Matrices

Question 1

define square matrix

Answer 1

A = B
(in terms of rows and columns)

Question 2

how do you notate a matrices

Answer 2

with a bold 𝐀 or a double underlined A

Question 3

What is trace tr(A) in a matrix?

Answer 3

the sum of the diagonal elements of the matrix
a(11) + a(22) + a(33) + a(…)

Question 4

Upper triangular matrix (𝐔)

Answer 4

all elements below the leading diagonal are zero

Question 5

Lower triangular matrix (𝐋)

Answer 5

all elements above the leading diagonal are zero

Question 6

Diagonal matrix (𝐃)

Answer 6

all elements outside the leading diagonal are zero

Question 7

unit matrix (𝐈)

Answer 7

all the diagonal elements are equal to 1 and all the other elements are zero

Question 8

zero matrix (𝟎)

Answer 8

all its elements equal to zero

Question 9

how do you transpose (𝐀^T) a matrix

Answer 9

by interchanging rows into columns and vice versa

Question 10

when is a matrix said to be symmetrical

Answer 10

when 𝐀^T = 𝐀

Question 11

How do you know if multiplying rectangular matrices is possible

Answer 11

Write the dimensions of both matrices, if the number of columns in the first is equal to the number of rows in the second then it is possible.
[3x2] and [2x4] = possible (as 2s are the same)
[2x3] and [4x2] = not possible (as 3 and 4 are different)

Question 12

Determine the relevant signs attached to the cofactor of a minor

Answer 12

|+ - + |
|- + - |
|+ - + |

Question 13

Laplace Expansion

Answer 13

‘Same as Cross product’ (look at rev card if forgotten)

Question 14

How do you find the determinate of a matrice

Answer 14

laplace expansion

Question 15

What are the requirements for a matrice to have an inverse

Answer 15

• It’s must be a square matrice
• it’s determinant (laplace expansion) can’t equal zero A ≠ 0

Question 16

How do you find the cofactors of a matrix

Answer 16

Find the minor of the matrix and add the appropriate sign

Question 17

What are the steps to find the inverse of a matrix

Answer 17

1. Find the determinant
2. Find the cofactor of the matrix
3. Transpose to get the adjoint
4. Divide it by the determinant

Question 18

How do you rearrange the equation A x = b (where x and b are vectors) to make x the subject

|a b c| |x| |p|
|d e f | |y| = |q| becomes A x = b
|l m n| |z| |r|

Answer 18

Multiple both sides by the inverse

(A x)(A^-1) = (b)(A^-1)
—>
x = A^-1b

Question 19

How do you find the determinate of a 4x4 matrix

Answer 19

Set the first row as the coefficients so make four 3x3 sub matrices