alleryStart learning →If A is a 3×3 matrix and det(A) = 4, then det(adj A):
- 4
- 16
- 8
- 64
Show answer and solution
Correct answer: B. 16
For n × n matrix: det(adj A) = (det A)^(n-1).
For n=3: det(adj A) = 4² = 16.
Indian Navy Pilot Matrices — practice questions
Explore 28 free Matrices questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Matrices with Quill →Matrices questions and exercises with answers
Showing questions 1–28 of 28.
If A is a 3×3 matrix and det(A) = 4, then det(adj A):Read the answer and worked solution →For a 2x2 matrix A with det A = 0, the system Ax = 0 has:Read the answer and worked solution →By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:Read the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Symmetric or skew symmetric?Read the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →Complete the equality conditionRead the answer and worked solution →Order the steps: is AB defined, and what order is it?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Special square matricesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →
Worked practice questions
For a 2x2 matrix A with det A = 0, the system Ax = 0 has:
- Only trivial solution
- INFINITELY many non-trivial solutions
- Exactly two solutions
- No solution
Show answer and solution
Correct answer: B. INFINITELY many non-trivial solutions
det A = 0 means A is singular (not invertible).
Homogeneous system Ax = 0 has nontrivial solutions exactly when A is singular.
With det A = 0, infinitely many solutions exist.
By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:
- $\det(A)/\det(A_1)$ (inverted)
- $\det(A_1)/\det(A)$ (correct ratio)
- $A_1 \cdot b$ (dot product)
- $\det(b)/\det(A)$ (b as matrix)
Show answer and solution
Correct answer: B. $\det(A_1)/\det(A)$ (correct ratio)
**Cramer's rule:** x_i = det(A_i)/det(A), where A_i is the matrix A with the i-th column replaced by b.
Requires det(A) ≠ 0 for unique solution.
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