VGLA term 1

Question 1

A system when b1 = b2 = ··· = bm = 0  is called

Accepted Answer

Homogeneous

Answer

Non-homogeneous

Question 2

A system is said to be homogeneous when b1 = b2 = ·· ·= bm = 0

Answer

true

Question 3

Homogeneous systems always have at least one solution called “the trivial solution”

Answer

true

Question 4

Homogeneous systems don't have solutions

Answer

true

Question 5

Number of rows

Accepted Answer

m

Answer

n

Question 6

Number of columns

Accepted Answer

n

Answer

m

Question 7

( 5 6 7 8 ) is a 1 x 4 matrix

Answer

true

Question 8

( 5 6 7 8 ) is a 4 x 1 matrix

Answer

true

Question 9

( 5 6 7 8 9 ) is a 5 x 1 matrix

Answer

true

Question 10

( 5 6 7 8 9 ) is a 1 x 5 matrix

Answer

true

Question 11

The matrix   1  
                      2  
                      3 
                      4 
Is a 1 x 4 matrix

Answer

true

Question 12

The matrix   1  
                      2  
                      3 
                      4 
Is a 4 x 1 matrix

Answer

true

Question 13

What is the order of The matrix   1  
                                                           2  
                                                           3 
                                                           4

Accepted Answer

4 x 1

Answer

1 x 4

Answer

4

Answer

1

Question 14

Two matrices A and B are equal if and only if:

Accepted Answer

Both have the same dimension say m x n 
aij = bij for all i,j.

Answer

Both have the same dimension say m x n 
a = bij for all i,j.

Answer

Both have the same dimension say m x n 
aij = bij for some i,j.

Answer

Both have the same dimension say m x n 
aij = b for all i,j.

Question 15

A + (-A) =

Accepted Answer

0mxn

Answer

0

Answer

A

Answer

A-A

Question 16

Matrix Multiplication Is Not Commutative

Answer

true

Question 17

Matrix Multiplication Is Commutative

Answer

true

Question 18

Matrix Multiplication Is Not Associative

Answer

true

Question 19

Matrix Multiplication Is Associative

Answer

true

Question 20

What does it mean for matrix multiplication to be associative ?

Accepted Answer

ABC = A(BC) = (AB)C

Answer

ABC = A(BC) = ABC

Answer

ABC = CBA

Answer

ABC = CBA = CAB = BCA

Question 21

An n × n matrix is diagonal when:  aij =0  for    i /= j

Answer

true

Question 22

An n × n matrix is diagonal when:  aij =0  for    i = j

Answer

true

Question 23

An upper triangular matrix is any n × n matrix where

Accepted Answer

aij =0 wherei > j

Answer

aij =0 where i /= j

Answer

aij =0 where i > i

Question 24

lower triangular matrix has:

Accepted Answer

aij =0 where j > i

Answer

aij =0 where j \> i

Answer

aij =0 where j = i

Question 25

If the n x n matrix A is invertible then

Accepted Answer

AB = In = BA

Answer

AB = In = BA-1

Answer

AB = BA

Answer

AB = In = B-1A-1

VGLA term 1

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