Matrices

37 solved questions from Class 12 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the domain, range, or fundamental theorem introduced in 'Matrices' (Class 12 Mathematics)? medium MCQ Functions & Theorems
• 2 What is the derivative or integral formula associated with 'Matrices'? medium MCQ Calculus & Formulae
• 3 How do you find the solution set or optimum value in 'Matrices'? medium MCQ Problem Solving & Optimization
• 4 Find all real values of k for which the system x+y+z=2, 2x+3y+kz=5, 3x+4y+(k+1)z=7 has infinitely many solutions. hard 5 marks Condition for infinite solutions using rank and determinant
• 5 For the system x+2y-z=3, 2x+4y-2z=6, 3x+6y-5z=2, find the rank of the coefficient matrix and the augmented matrix and state whether the system is consistent. If it is consistent, give the solution. medium 3 marks Rank of matrix and consistency of linear system
• 6 Consider the matrix A=2 -3 -3 5. Which of the following statements is true? easy MCQ 1 mark Symmetric matrix test
• 7 Solve the simultaneous equations 2x+y=7 and 3x-2y=4 using the matrix inverse method. medium 2 marks Inverse of a 2×2 matrix to solve linear equations
• 8 Determine the rank of the matrix D=1 2 3 2 4 6 3 6 9 and state whether the system Dx=5 10 15 is consistent. medium 2 marks Rank of a matrix and consistency of a linear system
• 9 The matrix C=4 7 2 5 is inverted and then used to solve the system 4x+7y=3, 2x+5y=1. Which of the following gives the correct solution? medium MCQ 2 marks Inverse of a 2x2 matrix and solving linear equations
• 10 Find the determinant of the matrix B=1 2 3 0 -1 4 5 0 2. easy 1 mark Determinant of a 3x3 matrix
• 11 For which real values of k is the matrix E=k 1 2 0 k-1 3 0 0 k-2 singular? For each such k, discuss the solvability of Ex=1 2 3. hard 3 marks Determinant of triangular matrix and solvability of singular systems
• 12 For which real values of k is the upper‑triangular matrix E=k 1 2 0 k-1 3 0 0 k-2 singular? For each such k, discuss whether the system Ex=1 2 3 has a solution. hard 5 marks Singular triangular matrix and solvability of linear system
• 13 Find the determinant of the matrix A=2 -1 3 0 5 -2 4 1 0. easy 2 marks Determinant of a 3x3 matrix
• 14 The matrix M=3 1 2 4 is inverted. Using the inverse, solve the system 3x+y=5 and 2x+4y=6. Which of the following gives the correct solution? medium MCQ 3 marks Matrix inverse method to solve linear equations
• 15 Determine the rank of the matrix R=1 2 3 2 4 5 3 6 9 and state whether the system Rx=7 14 21 is consistent. hard 4 marks Rank of matrix and consistency of linear system
• 16 Calculate the determinant of the matrix Q=3 0 -2 1 4 5 -1 2 0. medium 3 marks Determinant of a $3\times3$ matrix
• 17 Find the rank of the matrix P=1 2 4 2 4 8 3 6 12 and state whether the linear system Px=5 10 15 is consistent. easy 2 marks Rank and consistency of a linear system
• 18 For which real values of λ does the upper‑triangular matrix F=λ 2 1 0 λ-3 4 0 0 λ+2 become singular? For each such λ, discuss whether the system Fx=3 -1 2 has a solution. hard 5 marks Singular matrices with a parameter and consistency
• 19 Find the determinant of the matrix A=2 -1 3 0 4 5 1 2 0. easy 2 marks Determinant of a 3×3 matrix
• 20 Solve the simultaneous equations 4x+7y=6 and 2x+5y=3 using the matrix inverse method. medium 3 marks Inverse of a 2×2 matrix to solve linear equations
• 21 Consider the upper‑triangular matrix C=λ 1 4 0 λ-2 5 0 0 λ+1. Find all real values of λ for which C is singular. For each such λ, discuss whether the system Cx=2 -3 4 has a solution. hard 5 marks Singular matrix and solvability of linear system
• 22 Let B=1 2 3 4 2 4 6 8 3 6 9 12 and b=5 10 15. Determine the rank of B and state whether the system Bx=b is consistent. medium MCQ 3 marks Rank and consistency of a linear system
• 23 Find the determinant of the matrix A=5 2 3 -4. easy 1 mark Determinant of a $2\times2$ matrix
• 24 Solve the system 3x - y = 7, 2x + 4y = -2 using the matrix inverse method. Choose the correct ordered pair (x, y). medium MCQ 2 marks Inverse of a $2\times2$ matrix to solve linear equations
• 25 For the matrix B=1 2 3 4 2 4 6 8 0 1 1 0 and the column vector b=10 20 3, determine (i) the rank of the coefficient matrix, (ii) the rank of the augmented matrix [B|b], and (iii) whether the linear system Bx=b is consistent. If consistent, state the nature of the solution set. medium 3 marks Rank of matrix and consistency of linear system
• 26 Consider the upper‑triangular matrix D=λ 2 1 0 λ-4 5 0 0 λ+3.\n(a) Find all real values of λ for which D is singular.\n(b) For each such λ, discuss whether the system Dx=1 -2 3 has a solution.\n(c) If D is non‑singular, express the solution x= (x, y, z)^T in terms of λ. hard 4 marks Singularity of triangular matrix and solvability
• 27 What is the determinant of the matrix A=4 -1 2 3? easy 2 marks Determinant of 2×2 matrix
• 28 Consider the parameter matrix D=λ 2 1 0 λ-5 4 0 0 λ+2. (a) Find all real values of λ for which D is singular. (b) For each such λ, determine whether the system Dx=1 -2 3 has a solution. If it has, describe the solution set. hard 4 marks Singular upper‑triangular matrix and solution existence
• 29 For the matrix B=1 2 3 2 4 6 3 6 9 and the vector b=6 12 18, determine the rank of B and state whether the linear system Bx=b is consistent. If consistent, give the general solution. medium 3 marks Rank and consistency of a linear system
• 30 Determine the rank of the matrix B=1 2 3 2 4 6 3 5 9 and state whether the system Bx=7 14 21 is consistent. If consistent, describe the solution set. medium 2 marks Rank and consistency of a linear system
• 31 Solve the system 3x+4y=13, 2x-y=1 using the matrix inverse method. medium MCQ 2 marks Solving linear equations by matrix inverse
• 32 Find the determinant of the matrix A=1 2 0 -3 4 5 2 -1 3. easy 1 mark Determinant of a 3×3 matrix
• 33 Consider the upper‑triangular matrix D=λ 2 1 0 λ-5 4 0 0 λ+2. (a) Find all real values of λ for which D is singular. (b) For each such λ, discuss whether the system Dx=1 -2 3 has a solution. hard 4 marks Singularity of parameter matrix and consistency of linear system
• 34 Find the determinant of the matrix M=7 3 2 5. easy 1 mark Determinant of a $2\times2$ matrix
• 35 Solve the linear system 3x+4y=10 2x-y=3 using the matrix inverse method. medium 2 marks Solving linear equations using matrix inverse
• 36 For the matrix B=1 2 3 4 6 5 9, determine the rank and decide whether the system Bmathbfx=7 4 1 is consistent. If consistent, give the general solution. hard 3 marks Rank, consistency, and general solution of a linear system
• 37 Consider the upper‑triangular matrix D=λ 2 1 λ-5 4 0 λ+2. (a) Which values of λ make D singular? (b) For each such value, does the system Dmathbfx=1 2 have a solution? (c) If D is nonsingular, express the solution x in terms of λ. Choose the correct answer from the options below. hard MCQ 4 marks Determinant of upper‑triangular matrix and solvability of linear system