Worksheetslinear algebra
Total questions: 20
Worksheet time: 7mins
Which of the following is a scalar quantity?
A row vector
A single numbeR
A column vector
A matrix
The determinant of a 2×2 matrix
[acbd] is:
a+b+c+d
ab−cd
ad−bc
ac−bd
The dot product of two orthogonal vectors is:
0
1
-1
Undefined
Eigenvalues of an identity matrix are always:
Both 1 and -1
-1
0
1
Which of the following is true for symmetric matrices?
A2=I
A=−AT
A=AT
AT=0
If vector u=(3,4), then its magnitude is:
5
25
12
7
The inverse of the identity matrix is:
Zero matrix
Not defined
Determinant of the matrix
Identity matrix itself
If two vectors are linearly dependent, it means:
One is a scalar multiple of the other
They have the same magnitude
They must be orthogonal
They are perpendicular
Which of the following is a property of determinants?
det(A)=det(AT)−1
det(A+B)=det(A)⋅det(B)
det(AB)=det(A)⋅det(B)
det(AB)=det(A)+det(B)
The eigenvalues of a triangular matrix (upper or lower) are:
Always zero
Equal to the trace
Equal to its diagonal elements
Equal to the determinant
If vector u=(1,2,2) and vector v=(2,4,4), then they are:
Linearly dependent
Orthogonal
Linearly independent
Equal vectors
The number of linearly independent columns of a matrix is called:
Trace
Determinant
Rank
Nullity
What is the determinant of the identity matrix of size 4×4?
1
4
16
0
Which of these represents a unit vector?
(3,4)
(2,2)
(1,0)
(5,5)
A matrix is said to be singular if:
Its trace = 0
Its determinant = 0
It is diagonal
It is symmetric
Which of these is true about identity matrix I?
AI=0
AI=A
AI=I
AI=AT
The rank of the identity matrix of order 3 is:
0
1
2
3
Which of the following is true for an orthonormal set of vectors?
Vectors are both orthogonal and normalized
Vectors are normalized but not orthogonal
Vectors are orthogonal but not normalized
Vectors are linearly dependent
The eigenvectors of a symmetric matrix are always:
Undefined
Orthogonal
Complex numbers
Linearly dependent
Which of the following is an orthogonal pair of vectors?
(1, 0), (0, 1)
(1, 2), (2, 4)
(3, 3), (3, 3)
(2, 2), (4, 4)
