If A and B are matrices of same order, then (AB' – BA') is a
skew-symmetric matrix
null matrix
symmetric matrix
None of the above
Correct Answer
Option 1
Solution
We have,
(AB' - BA') if we calculate (AB' - BA')'
⇒ (AB' - BA')' = (AB')' - (BA')'
⇒ (AB' - BA')' = (B')' A' - (A')' B' {(AB)' = B'A'}
⇒ (AB' - BA')" = B A' - A B' {(A')' = A}
⇒ (AB' - BA')' = - (AB' - BA')
Hence (AB' - BA') is a skew-symmetric matrix.
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
If A is a square matrix of order 3 such that |A| = 3, then adj (adj A) is:
27A
3A
9A
A
Correct Answer
Option 2
Solution
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
If is an idempotent matrix, then which of the following is true
a = 1
a = 4
∣A∣ = 0
∣A∣ = 2
Correct Answer
Option 3
Solution
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Use the rules on the determinants of block matrices to compute the determinant of the matrix
-18
-16
16
0
Correct Answer
Option 2
Solution
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Derive the complementary projection matrix (onto S2) and use it to find the projection onto S2 of the vector
Correct Answer
Option 2
Solution
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
95125
Correct Answer
Option 1
Solution
Sn = 95125
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
-25
-15
-1/15
None of the above
Correct Answer
Option 3
Solution
k = -1/15
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Choose the correct option:
Singular
Idempotent
Skew-symmetric
Involuntary
Correct Answer
Option 1,2
Solution
∴ matrix M is singular
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
0
Correct Answer
Option 1
Solution
Hence, |A^121 - A^120| = A^120|A – I| = 0
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A square matrix A is said to be an idempotent matrix if A^2 = A. If A and B are idempotent matrices and AB = BA, then which of the following is an idempotent matrix
A+B
A-B
AB
B-A
Correct Answer
Option 3
Solution
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
If B is an idempotent matrix, and A = I - B then
Choose the correct options:
A^2 = A
A^2 = I
AB = 0
BA = 0
Correct Answer
Option 1,3,4
Solution
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A square matrix A is said to be an idempotent matrix if A^2 = A. If A is a non-singular idempotent matrix, then
A + A’ = 0
A = 0
A = In (identity matrix)
None of the above
Correct Answer
Option 3
Solution
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
-0.8
-0.5
0.5
1
Correct Answer
Option 1
Solution
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Which of the following matrix projects every vector b in R^3 onto the line in the direction of
a = (2, 1, 3):
Correct Answer
Option 4
Solution
The general formula for the orthogonal projection onto the column space of a matrix A is