Question 1
Question
A system when b1 = b2 = ··· = bm = 0 is called
Answer
-
Homogeneous
-
Non-homogeneous
Question 2
Question
A system is said to be homogeneous when b1 = b2 = ·· ·= bm = 0
Question 3
Question
Homogeneous systems always have at least one solution called “the trivial solution”
Question 4
Question
Homogeneous systems don't have solutions
Question 5
Question 6
Question
Number of columns
Question 7
Question
( 5 6 7 8 ) is a 1 x 4 matrix
Question 8
Question
( 5 6 7 8 ) is a 4 x 1 matrix
Question 9
Question
( 5 6 7 8 9 ) is a 5 x 1 matrix
Question 10
Question
( 5 6 7 8 9 ) is a 1 x 5 matrix
Question 11
Question
The matrix 1
2
3
4
Is a 1 x 4 matrix
Question 12
Question
The matrix 1
2
3
4
Is a 4 x 1 matrix
Question 13
Question
What is the order of The matrix 1
2
3
4
Question 14
Question
Two matrices A and B are equal if and only if:
Answer
-
Both have the same dimension say m x n
aij = bij for all i,j.
-
Both have the same dimension say m x n
a = bij for all i,j.
-
Both have the same dimension say m x n
aij = bij for some i,j.
-
Both have the same dimension say m x n
aij = b for all i,j.
Question 15
Question 16
Question
Matrix Multiplication Is Not Commutative
Question 17
Question
Matrix Multiplication Is Commutative
Question 18
Question
Matrix Multiplication Is Not Associative
Question 19
Question
Matrix Multiplication Is Associative
Question 20
Question
What does it mean for matrix multiplication to be associative ?
Answer
-
ABC = A(BC) = (AB)C
-
ABC = A(BC) = ABC
-
ABC = CBA
-
ABC = CBA = CAB = BCA
Question 21
Question
An n × n matrix is diagonal when: aij =0 for i /= j
Question 22
Question
An n × n matrix is diagonal when: aij =0 for i = j
Question 23
Question
An upper triangular matrix is any n × n matrix where
Answer
-
aij =0 where i /= j
-
aij =0 wherei > j
-
aij =0 where i > i
Question 24
Question
lower triangular matrix has:
Answer
-
aij =0 where j > i
-
aij =0 where j \> i
-
aij =0 where j = i
Question 25
Question
If the n x n matrix A is invertible then
Answer
-
AB = In = BA
-
AB = In = BA-1
-
AB = BA
-
AB = In = B-1A-1