0.10 Matrices and linear systems
Unit 0 · Textbook foundations: equations, lines and systems
Ideas in this lesson
Matrix addition
Add corresponding entries only for matrices with equal dimensions.
Matrix multiplication
Each product entry is a row-column dot product; order matters.
Determinants
For a two-by-two matrix, subtract the product of the off-diagonal entries from the diagonal product.
Inverse matrices
A nonzero determinant permits an inverse; verify its product with the original is the identity.
Solve with inverses and Cramer’s rule
Use the nonzero coefficient determinant to solve by inverse multiplication or determinant ratios.
Scalar multiplication of matrices
Multiply every entry by the stated scalar and retain the matrix dimensions.
Matrix subtraction
Subtract corresponding entries and retain the subtraction signs for negative entries.
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