Matrices

Question 1

Singular matrix

Answer 1

the determinant is zero

Question 2

Symmetric matrix

Answer 2

when the matrix equals its own transpose

Question 3

Trace of a matrix

Answer 3

the sum of the elements of the main diagonal

(square matrices only)

Question 4

Inconsistent system of linear equations

Answer 4

it has no solutions

Question 5

Consistent system of linear equations

Answer 5

it has a solution

Question 6

Homogenous system

Answer 6

a system of linear equations having matrix form AX=0 (0 represents a zero column matrix)

Question 7

Inhomogenous system

Answer 7

a system of linear equations having matrix form AX=b (b is non-zero column vector)

Question 8

When are a system of equations linearly dependent?

Answer 8

when one row is a multiple of another or the sum of multiples of other rows

Question 9

Commutative property

Answer 9

order changes but answer doesn’t

Question 10

Associative property

Answer 10

(grouping) changes but answer doesn’t

Question 11

Commutative example

Answer 11

A+B=B+A

Question 12

Associative example

Answer 12

(A+B)C=A(B+C)

Question 13

What are the steps for finding the inverse of a 3x3 matrix?

Answer 13

• find detA
• find the matrix of minors (M)
• find the matrix of cofactors (C)
• transpose the matrix of cofactors (C^t)
• use 1/ detA C^t to find A^-1

Question 14

What is the matrix of minors?

Answer 14

you replace every element in a matrix by its minor

Question 15

What is the matrix of cofactors?

Answer 15

including the sign changes (+-+-)

Question 16

How do you transpose the matrix of cofactors?

Answer 16

Interchange the columns and rows so first row becomes first column, etc

Question 17

How do you know if a system of linear equations is consistent or not?

Answer 17

if it is consistent, there will be at least one set of values that satisfies all of the equations simultaneously. If not, they are inconsistent.

Question 18

How do you know if equations will be consistent or not when det m = 0

Answer 18

• use two equations and cancel out a term to give 2 different, 2 term equations.
• if you can simplify or multiply them by a number to make them the same, they are consistent.
• if you can make the coefficients the same but not the answers, they are inconsistent

Question 19

Generally for a system of linear equations, what does D≠0 mean for the solution?

Answer 19

there is a single, unique solution