1300

Question 1

Consistent linear equations

Answer 1

Have one or more solutions

Question 2

Inconsistent linear equations

Answer 2

Have no solutions

Question 3

System of linear equations

Answer 3

No exponents, indices, trigonometric function, etc. with variables

Question 4

Justify that an equation is linear

Answer 4

Show that it is in the form of a linear equation and identify all the coefficients

Question 5

A + B

Answer 5

= B + A

Question 6

A + (B + C) =

Answer 6

(A + B) + C

Question 7

A(BC) =

Answer 7

(AB)C

Question 8

A(B + C) =

Answer 8

AB + AC

Question 9

(B + C)A =

Answer 9

BA + CA

Question 10

A(B − C) =

Answer 10

AB − AC

Question 11

(B − C)A =

Answer 11

BA − CA

Question 12

a(B + C) =

Answer 12

aB + aC

Question 13

a(B − C) =

Answer 13

aB − aC

Question 14

(a + b)C =

Answer 14

aC + bC

Question 15

(a − b)C =

Answer 15

aC − bC

Question 16

a(bC) =

Answer 16

(ab)C

Question 17

a(BC) =

Answer 17

(aB)C = B(aC)

Question 18

A + 0 = (for zero matrices)

Answer 18

0 + A = A

Question 19

A − 0 = (for 0 matrices)

Answer 19

A

Question 20

A − A = (for 0 matrices)

Answer 20

A + (−A) = 0

Question 21

0A = (for 0 matrices)

Answer 21

0

Question 22

If cA = 0 for 0 matrices

Answer 22

then c = 0 or A = 0

Question 23

If A is a square matrix, and if a matrix B of the same size can be found such that AB = BA = I ,

Answer 23

then A is said to be invertible

and B is called an inverse of A.

Question 24

Formula of the inverse of a 2 by 2 matrix

Answer 24

A−1 = 1 (ad − bc) times I d −b I

I −c a I

Question 25

A matrix E is called an elementary matrix if

Answer 25

it can be obtained from an identity matrix by performing a single elementary row operation

Question 26

If A is an n × n matrix, then the following statements are equivalent, that is, all true or all false

Answer 26

(a) A is invertible. (b) Ax = 0 has only the trivial solution. (c) The reduced row echelon form of A is In. (d) A is expressible as a product of elementary matrices

Question 27

Inversion Algorithm

Answer 27

To find the inverse of an invertible matrix A, find a sequence of elementary row operations that reduces A to the identity and then perform that same sequence of operations on In to obtain A−1