Matrix Questions Practice PDF

Matrix Questions for Practice 1. Matrix Addition and Subtraction Given: A = [[3, 5], [1, 4]], B = [[2, -1], [0, 3]] Find: A + B and A - B. 2. Scalar Multiplication Find 3A, where: A = [[2, 1], [-1, 4]]. 3. Matrix Multiplication Given: A = [[1, 2], [3, 4]], B =...

Matrix Questions for Practice 1. Matrix Addition and Subtraction Given: A = [[3, 5], [1, 4]], B = [[2, -1], [0, 3]] Find: A + B and A - B. 2. Scalar Multiplication Find 3A, where: A = [[2, 1], [-1, 4]]. 3. Matrix Multiplication Given: A = [[1, 2], [3, 4]], B = [[2, 0], [1, 3]] Find: AB. 4. Determinants Find the determinant of: A = [[5, 3], [-2, 4]]. Use the formula: det(A) = ad - bc. 5. Inverse of a Matrix Find the inverse of: A = [[1, 2], [3, 4]] if it exists, using:  A^(-1) = (1/det(A)) * [[d, -b], [-c, a]]. 6. Solve System of Equations Using Matrices Solve the following system of equations using the matrix method: 2x + 3y = 13, x - 2y = -3 Represent this as: A = [[2, 3], [1, -2]], X = [[x], [y]], B = [, [-3]]. Find X = A^(-1)B. 7. Singular Matrix Check if the matrix is singular: A = [[2, 4], [1, 2]]. A matrix is singular if det(A) = 0. 8. Adjoint of a Matrix Find the adjoint of: A = [[1, 3], [2, 4]]. The adjoint is given by: Adj(A) = [[d, -b], [-c, a]]. 9. Verification of Properties Verify: det(AB) = det(A) * det(B) where: A = [[1, 0], [0, 1]], B = [[2, 3], [4, 5]]. 10. Application Problem The cost of 2 pens and 3 notebooks is $50, and the cost of 1 pen and 2 notebooks is $30. Represent this as: 2x + 3y = 50, x + 2y = 30 Matrix form: A = [[2, 3], [1, 2]], X = [[x], [y]], B = [, ]. Solve using X = A^(-1)B.