Master fundamental matrix operations including addition, multiplication, determinants, and inverses. Learn to solve linear systems using matrix methods and apply these concepts to real-world problems.
Multiply the two 2×2 matrices!
Matrix A:
Matrix B:
Calculate the determinant of the 2×2 matrix!
Matrix:
Matrices can be added element-wise if they have the same dimensions. Scalar multiplication multiplies every element by a constant.
Given: A = [[2, 3], [1, 4]], B = [[1, 2], [3, 1]]
Step 1: Add corresponding elements
Step 2: A + B = [[2+1, 3+2], [1+3, 4+1]]
Answer: [[3, 5], [4, 5]]
Given: A = [[1, 2], [3, 4]], k = 3
Step 1: Multiply each element by 3
Step 2: 3A = [[3×1, 3×2], [3×3, 3×4]]
Answer: [[3, 6], [9, 12]]
Given: A = [[5, 2], [3, 1]], B = [[2, 1], [1, 2]]
Step 1: Subtract corresponding elements
Step 2: A - B = [[5-2, 2-1], [3-1, 1-2]]
Answer: [[3, 1], [2, -1]]