Add, multiply, and use matrices to solve systems of equations.
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices can be added (element-wise), multiplied (row-by-column), and used to represent and solve systems of linear equations.
Matrix multiplication: (AB)แตขโฑผ = sum of row i of A times column j of B. The product AB exists only when the number of columns in A equals the number of rows in B.
A = [[1,2],[3,4]], B = [[5,6],[7,8]]. AB = [[(1)(5)+(2)(7), (1)(6)+(2)(8)], [(3)(5)+(4)(7), (3)(6)+(4)(8)]] = [[19, 22],[43, 50]].
Solving AX = B Using the Inverse
What is the determinant of [[3, 4], [1, 2]]?