Matrices - Online Test
Q1. A square matrix A is called idempotent if
Answer : Option C
Explaination / Solution:
If the product of any square matrix with itself is the matrix itself , then the matrix is called Idempotent.
Q2. If is a square root of the identity matrix, then a, b, c satisfy the relation
Answer : Option B
Explaination / Solution:
⎡⎣⎢⎢⎢acb−a⎤⎦⎥⎥⎥⎡⎣⎢⎢⎢acb−a⎤⎦⎥⎥⎥=⎡⎣⎢⎢⎢1001⎤⎦⎥⎥⎥⇒a2+bc=1
Q3.
If A and B are invertible matrices of the same order, then is equal to
Answer : Option C
Explaination / Solution:
By the property of inverse is equal to .
Q4. If , then
Answer : Option A
Explaination / Solution:
If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.
Q5. If
Answer : Option C
Explaination / Solution:
If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.
Q6. Let A be any matrix, then can be found only when
Answer : Option B
Explaination / Solution:
The product of any matrix with itself can be found only when it is a square matrix.i.e. m=n.
Q7. If A and B are any two matrices, then
Answer : Option C
Explaination / Solution:
Let matrix A is of order m x n , and matrix B is of order p x q . then , the product AB is defined only when n = p. that’s why, If A and B are any two matrices, thenAB may or may not be defined.
Q8.
A square matrix A = is called a lower triangular matrix if for
Answer : Option A
Explaination / Solution:
Q9. A square matrix is called an upper triangular if for
Answer : Option A
Explaination / Solution:
Upper Triangular matrix is given by : Here, if i is greater than j.and , if I is less than j.
Q10. If, then for all natural numbers n, is equal to
Answer : Option D
Explaination / Solution:
