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JEE Advanced Matrices — practice questions — page 2

Explore 47 free Matrices questions in JEE Advanced 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 31–47 of 47.

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 →A matrix with 3 rows and 4 columns has how many elements?Read the answer and worked solution →If a matrix has 8 elements, the number of possible orders it can have is:Read the answer and worked solution →A matrix is called a square matrix when:Read the answer and worked solution →If $A$ is a matrix of order $m\times n$, then its transpose $A'$ has order:Read the answer and worked solution →A square matrix $A$ is symmetric if:Read the answer and worked solution →In a skew-symmetric matrix, all the diagonal elements are:Read the answer and worked solution →Two matrices can be added only if they have:Read the answer and worked solution →If $A$ is of order $2\times3$ and $B$ is of order $3\times4$, then $AB$ has order:Read the answer and worked solution →In a diagonal matrix, all the non-diagonal elements are:Read the answer and worked solution →For any matrix $A$, $(A')'$ equals:Read the answer and worked solution →In the identity matrix, the diagonal elements are 1 and all other elements are:Read the answer and worked solution →If $A=[a_{ij}]$ is a $3\times3$ matrix with $a_{ij}=i+j$, then the element $a_{23}$ is:Read the answer and worked solution →Match the matrix property to its definitionRead the answer and worked solution →Order the steps to find the inverse of a 2×2 matrixRead the answer and worked solution →Match the matrix type to its shorthandRead the answer and worked solution →

Worked practice questions

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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If A = [[1,1],[1,1]], the determinant and rank:

  1. det = 0, rank = 1
  2. det = 2, rank = 2
  3. det = 0, rank = 2
  4. det = 1, rank = 1
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Correct answer: A. det = 0, rank = 1

det = 1·1 - 1·1 = 0. Both rows identical, so only 1 linearly independent row. Rank = 1.

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A matrix with 3 rows and 4 columns has how many elements?

  1. 12
  2. 7
  3. 16
  4. 9
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Correct answer: A. 12

Number of elements = rows × columns = 3 × 4 = 12.

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