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JEE Main Matrices and Determinants — practice questions

Explore 89 free Matrices and Determinants questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Matrices and Determinants questions and exercises with answers

Showing questions 1–30 of 89.

A matrix is:Read the answer and worked solution →Identity matrix I has:Read the answer and worked solution →For matrix multiplication AB to be defined:Read the answer and worked solution →Determinant of 2×2 matrix [[a, b], [c, d]]:Read the answer and worked solution →Determinant of triangular (upper or lower) matrix:Read the answer and worked solution →A matrix is invertible iff:Read the answer and worked solution →For 2×2 matrix A = [[2,3],[1,4]], A⁻¹ =Read the answer and worked solution →Transpose of [[1,2,3],[4,5,6]] is:Read the answer and worked solution →For matrices A, B (square, same size): (AB)^T =Read the answer and worked solution →A matrix is symmetric if:Read the answer and worked solution →A matrix is skew-symmetric if:Read the answer and worked solution →Determinant of identity matrix I_n:Read the answer and worked solution →Determinant: if two rows are equal, det =Read the answer and worked solution →For matrix A with |A| = 5 and A is 3×3, |2A| =Read the answer and worked solution →For matrix A and its adjugate adj(A): A × adj(A) =Read the answer and worked solution →For non-singular A and scalar k: |k A^(-1)| = (A is n × n)Read the answer and worked solution →Solve: x + y + z = 6, 2x + y - z = 1, x - y + z = 2. Determinant of coefficient matrix:Read the answer and worked solution →If A is orthogonal (A A^T = I), then |A| =Read the answer and worked solution →For A = [[3, 1], [2, 4]], characteristic polynomial:Read the answer and worked solution →Eigenvalues of A = [[3,1],[2,4]]:Read the answer and worked solution →For matrix A, rank(A) + nullity(A) =Read the answer and worked solution →For A symmetric n×n matrix, all eigenvalues are:Read the answer and worked solution →Trace of matrix is sum of diagonal entries. For 2×2 [[a,b],[c,d]]:Read the answer and worked solution →System of equations Ax = b has unique solution iff:Read the answer and worked solution →For 3×3 matrix with rows R₁, R₂, R₃ = R₁ + 2R₂. Determinant =Read the answer and worked solution →If A is 3×3 with |A| = -2, then |adj(A)| =Read the answer and worked solution →Product of eigenvalues of square matrix A =Read the answer and worked solution →Match each matrix termRead the answer and worked solution →Key in the matrix answerRead 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 →

Worked practice questions

A matrix is:

  1. A vector
  2. A rectangular array of numbers arranged in rows and columns
  3. A single number
  4. A point
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Correct answer: B. A rectangular array of numbers arranged in rows and columns

**Matrix:** rectangular array of numbers in m rows × n columns. **Notation:** A_(ij) = element in row i, column j. Size denoted m × n.

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Identity matrix I has:

  1. 1s on diagonal, 0s elsewhere; AI = A for any A
  2. All 1s except diagonal
  3. All zeros
  4. All 1s
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Correct answer: A. 1s on diagonal, 0s elsewhere; AI = A for any A

Identity matrix I_n: square n × n with 1's on diagonal, 0's off-diagonal. **For any compatible A:** AI = A = IA. Multiplicative identity for matrices.

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For matrix multiplication AB to be defined:

  1. Both must be square
  2. A and B must be same size
  3. Number of columns of A must equal number of rows of B
  4. Both must be 2×2
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Correct answer: C. Number of columns of A must equal number of rows of B

AB defined when columns of A = rows of B. If A is m×p and B is p×n, then AB is m×n. Otherwise undefined.

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More Mathematics topics

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