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KEAM Matrices — practice questions — page 2

Explore 59 free Matrices questions in KEAM Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Matrices questions and exercises with answers

Showing questions 31–59 of 59.

Inverse of [[2,0],[0,3]]: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 →For a 3x3 matrix A: (A + Aᵀ) is always:Read the answer and worked solution →If A = [[1,1],[1,1]], the determinant and rank: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

Inverse of [[2,0],[0,3]]:

  1. [[1/2,0],[0,1/3]]
  2. [[2,0],[0,3]]
  3. [[3,0],[0,2]]
  4. [[1,0],[0,1]]
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Correct answer: A. [[1/2,0],[0,1/3]]

For diagonal matrix [[a,0],[0,b]], inverse is [[1/a, 0],[0, 1/b]]. **So [[2,0],[0,3]]⁻¹ = [[1/2,0],[0,1/3]].**

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For a 2x2 matrix A with det A = 0, the system Ax = 0 has:

  1. Only trivial solution
  2. INFINITELY many non-trivial solutions
  3. Exactly two solutions
  4. No solution
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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.

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For a 3x3 matrix A: (A + Aᵀ) is always:

  1. Skew-symmetric
  2. Symmetric
  3. Zero matrix
  4. Diagonal matrix
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Correct answer: B. Symmetric

We have (A + Aᵀ)ᵀ = Aᵀ + A. So (A + Aᵀ)ᵀ = A + Aᵀ. Same as original, so symmetric. Similarly (A - Aᵀ) is skew-symmetric.

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