Matrix products and determinants.
Example 1
A has rows (9,4) and (7,1). B has rows (2,0) and (1,3). Find the entry in row 1, column 1 of AB.
Switch pairs to follow the matching row and column entries.Show worked answer
Answer: 22
- Multiply row 1 of A by column 1 of B:9×2+4×1=22.
Example 2
Find the determinant of the matrix with rows (5,7) and (0,3).
Switch diagonals and compare the two products used in a determinant.Show worked answer
Answer: 15
- For a 2 by 2 matrix, determinant = top-left × bottom-right − top-right × bottom-left.
- Determinant =5×3−7×0=15.
Example 3
A=[[1,3],[2,7]]. Which is A−1?
Show worked answer
Answer: [[7,−3],[−2,1]]
- det A=7−6=1. Swap the diagonal entries and negate the off-diagonal entries.