If A=[[1,2],[3,4]] find det(A) and adj(A).
Get the complete, step-by-step math solution for: "If A = [[1, 2], [3, 4]] find det(A) and adj(A).". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Calculate the Determinant of A
For a 2×2 matrix A=(acbd), the determinant is calculated as the product of the elements on the main diagonal minus the product of the elements on the anti-diagonal. Here, a=1, b=2, c=3, and d=4.
Step 2: Substitute values and compute determinant
Substitute the values a=1, b=2, c=3, and d=4 into the determinant formula. This gives us (1)(4) - (2)(3), which simplifies to 4 - 6 = -2.
Step 3: Calculate the Adjoint of A
For a 2×2 matrix A=(acbd), the adjoint matrix is found by swapping the elements on the main diagonal (a and d) and changing the signs of the elements on the anti-diagonal (b and c).
Step 4: Substitute values into the adjoint formula
Substitute the values a=1, b=2, c=3, and d=4 into the adjoint formula. The element d becomes the top-left, a becomes the bottom-right, −b becomes the top-right, and −c becomes the bottom-left.