What is the inverse of the 2x2 matrix A = [[3, 2], [1, 1]]?
Answer and explanation
Correct answer: C. [[1, -2], [-1, 3]]
- Step 1: det(A) = (3)(1) - (2)(1) = 3 - 2 = 1. Step 2. Adjugate: swap diagonal entries (1 and 3) and negate off-diagonal entries (-2 and -1): adj(A) = [[1, -2], [-1, 3]]. Step 3. A^-1 = (1/det) adj(A) = [[1, -2], [-1, 3]]. Answer: [[1, -2], [-1, 3]]. Why not the others:* [[-1, 2], [1, -3]] has the wrong sign.
Practise more Algebra, Matrices and Trigonometry.
Free questions with an explanation for every one, and full timed ECAT Pakistan mock tests.
More Algebra, Matrices and Trigonometry questions
- What is the determinant of the 3x3 matrix with rows [1, 2, 3], [0, 4, 5], [0, 0, 6]?
- What is the sum to infinity of the geometric series 8 + 4 + 2 + 1 + ...?
- If sin(theta) + cos(theta) = 1, what is the value of sin(2*theta)?
- What is the general solution of the trigonometric equation cos(x) = 1/2?
- How many terms are in the algebraic expansion of (2x + 3y)^10?
- What is the value of the expression: arctan(1/2) + arctan(1/3)?