Determinants
Assertion & Reason Type Questions
Directions: In the following questions, each question contains Assertion (A) and
Reason (R). Each question has 4 choices (a), (b), (c) and (d) out of which only one is
correct. The choices are:
a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
b. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A)
c. Assertion (A) is true but Reason (R) is false
d. Assertion (A) is false but Reason (R) is true
Q1. Assertion (A): If a, b, c are distinct and x, y, z are not all zero, given that ax + by +
cz = 0, bx + cy + az = 0, cx + ay + bz = 0, then a + b + c ≠ 0.
Reason (R): a² + b² + c² > ab + bc + ca, if a, b and c are distinct.
Answer : (d) Assertion (A) is false but Reason (R) is true
Q2. Assertion (A): The determinant of a matrix
Reason (R): The determinant of a skew-symmetric matrix of odd order is zero.
Answer : (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
Q3. Assertion (A): If A is skew-symmetric matrix of order 3, then its determinant
should be zero.
Reason (R): If A is a square matrix, then det A = det A' = det (— A').
Answer : (c) Assertion (A) is true but Reason (R) is false
Q4. Assertion (A): ∆ = a11A11 + a12A12 + α13A13 where, Aij is cofactor of aij.
, Reason (R): ∆ = Sum of the products of elements of any row (or column) with their
corresponding cofactors.
Answer : (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
Q5. Let A be a 2 × 2 matrix.
Assertion (A): adj (adj A) = A
Reason (R): | adj A | = | A |
Answer : (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the
correct explanation of Assertion (A)
Q6.
Answer : (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the
correct explanation of Assertion (A)
Q7.
Answer : (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
Q8. Assertion (A): There are only finitely many 2 × 2 matrices which commute with the
matrix
Assertion & Reason Type Questions
Directions: In the following questions, each question contains Assertion (A) and
Reason (R). Each question has 4 choices (a), (b), (c) and (d) out of which only one is
correct. The choices are:
a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
b. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A)
c. Assertion (A) is true but Reason (R) is false
d. Assertion (A) is false but Reason (R) is true
Q1. Assertion (A): If a, b, c are distinct and x, y, z are not all zero, given that ax + by +
cz = 0, bx + cy + az = 0, cx + ay + bz = 0, then a + b + c ≠ 0.
Reason (R): a² + b² + c² > ab + bc + ca, if a, b and c are distinct.
Answer : (d) Assertion (A) is false but Reason (R) is true
Q2. Assertion (A): The determinant of a matrix
Reason (R): The determinant of a skew-symmetric matrix of odd order is zero.
Answer : (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
Q3. Assertion (A): If A is skew-symmetric matrix of order 3, then its determinant
should be zero.
Reason (R): If A is a square matrix, then det A = det A' = det (— A').
Answer : (c) Assertion (A) is true but Reason (R) is false
Q4. Assertion (A): ∆ = a11A11 + a12A12 + α13A13 where, Aij is cofactor of aij.
, Reason (R): ∆ = Sum of the products of elements of any row (or column) with their
corresponding cofactors.
Answer : (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
Q5. Let A be a 2 × 2 matrix.
Assertion (A): adj (adj A) = A
Reason (R): | adj A | = | A |
Answer : (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the
correct explanation of Assertion (A)
Q6.
Answer : (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the
correct explanation of Assertion (A)
Q7.
Answer : (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A)
Q8. Assertion (A): There are only finitely many 2 × 2 matrices which commute with the
matrix
