Matrices and algebra of matrices - One Line Questions
1.
What is the identity matrix of order 2x2? —
[[1, 0], [0, 1]]
2.
If A = [[3, 2], [1, 4]] and B = [[1, -2], [-3, 5]], what is A - B? —
[[2, 4], [4, -1]]
3.
If A = [[1, 2], [3, 4]], what is 2A? —
[[2, 4], [6, 8]]
4.
If A = [[1, 2], [3, 4]] and B = [[-1, 0], [2, 1]], what is AB? —
[[2, 2], [10, 6]]
5.
If A = [[1], [2], [3]] and B = [[4, 5, 6]], what is AB? —
[[4, 5, 6], [8, 10, 12], [12, 15, 18]]
6.
If A = [[1, 2, 3]] and B = [[4], [5], [6]], what is AB? —
[[32]]
7.
If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is A + B? —
[[6, 8], [10, 12]]
8.
If A = [[a, b], [c, d]], then -A is: —
[[-a, -b], [-c, -d]]
9.
If A = [[1, 0], [0, 1]] and B = [[x, y], [z, w]], then AB is: —
[[x, y], [z, w]]
10.
For a skew-symmetric matrix, the diagonal elements are always: —
0
11.
What is the order of the product of a 2x3 matrix and a 3x2 matrix? —
2x2
12.
What is the order of a matrix if it has 3 rows and 4 columns? —
3x4
13.
What is the sum of elements of a matrix A = [[2, -1], [3, 5]]? —
11
14.
If A is a square matrix, then (A^T)^T is equal to: —
A
15.
If A is a matrix, then A * 0 (where 0 is the null matrix of appropriate order) is: —
0
16.
A square matrix A is called symmetric if: —
A = A^T
17.
A square matrix A is called skew-symmetric if: —
A = -A^T
18.
What is the transpose of a matrix A, denoted by A^T? —
A matrix obtained by interchanging rows and columns.
19.
If A is a square matrix, A + A^T is always: —
A symmetric matrix
20.
If A is a square matrix, A - A^T is always: —
A skew-symmetric matrix
21.
If A and B are matrices of the same order, then (A + B)^T is equal to: —
A^T + B^T
22.
If A = [[a, b], [c, d]], what is the determinant of A? —
ad - bc
23.
A scalar matrix is a diagonal matrix where: —
All diagonal elements are equal.
24.
An identity matrix is a scalar matrix where: —
All diagonal elements are one.
25.
Matrix multiplication is: —
Not always commutative (AB may or may not be equal to BA)
26.
If A is an m x n matrix and B is an n x m matrix, then AB and BA are: —
Not necessarily of the same order
27.
If A and B are matrices such that AB and BA are defined, then (AB)^T is equal to: —
B^T * A^T
28.
A matrix with only one row is called a: —
Row Matrix
29.
Which property states that for matrices A, B, and C (of appropriate orders), A(BC) = (AB)C? —
Associative Property
30.
Which property states that for matrices A, B, and C (of appropriate orders), A(B + C) = AB + AC? —
Distributive Property
31.
Which of the following is a property of matrix addition? —
All of the above
32.
The sum of elements on the main diagonal of a square matrix is called its: —
Trace
33.
If A is a square matrix such that A^2 = I (Identity Matrix), then A is called: —
Involutory Matrix
34.
If A is a square matrix such that A^k = 0 (Null Matrix) for some positive integer k, then A is called: —
Nilpotent Matrix
35.
A matrix where all elements are zero is called a: —
Null Matrix
36.
If A is a square matrix and k is a scalar, then Trace(kA) is equal to: —
k * Trace(A)
37.
If A is an m x n matrix, then A^T is an: —
n x m matrix
38.
If A is an m x n matrix and B is an n x p matrix, what is the order of the product AB? —
m x p
39.
If A is a square matrix such that A^2 = A, then A is called: —
Idempotent Matrix
40.
If A is any matrix and I is the identity matrix of appropriate order, then AI is equal to: —
A
41.
Which of the following is NOT a type of matrix? —
Circular Matrix
42.
A matrix with only one column is called a: —
Column Matrix
43.
A matrix where the number of rows equals the number of columns is called a: —
Square Matrix
44.
For a matrix A, if A = A^T, then A is: —
Symmetric
45.
For a matrix A, if A = -A^T, then A is: —
Skew-Symmetric
46.
What is the condition for two matrices to be equal? —
They must have the same order and corresponding elements must be equal.
47.
If A and B are matrices of the same order, then Trace(A + B) is equal to: —
Trace(A) + Trace(B)
48.
Which of the following is true for matrices A and B for which AB is defined? —
Trace(AB) = Trace(BA)
49.
Any square matrix can be expressed as the sum of: —
A symmetric and a skew-symmetric matrix