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1 chapter · 11 notes · all free

1. Matrices and Their TypesIs the matrix with 3, 3, 3 on its diagonal diagonal, scalar or identity? Can you name every kind that fits?
2. Transpose, Symmetric and Other Special MatricesSquare a matrix: which one comes back as itself, which one turns to zero, which one to I?
3. Equality, Addition, Subtraction and Scalar Multiples of MatricesCan you tell which two matrices can be added without reading a single entry?
4. Multiplication of Matrices and PowersAB exists, so why can BA fail to exist?
5. Determinants and Finding Their ValueHow can one determinant give 21 by four different routes, and which route is the least work?
6. Minors and Cofactors of a DeterminantWhy does a determinant's sum come out zero when you use the wrong row's cofactors?
7. Properties of DeterminantsSwap two rows of a determinant and what happens to its value? You can say it without expanding.
8. Using the Properties: Values, Proofs and EquationsNearly every sum in exercise 1(B) opens with one of four moves. Which move fits which sum, tried by hand.
9. Singular and Non-singular Matrices and the Idea of an InverseOne number tells you whether a matrix can be inverted. Which number?
10. Adjoint, Finding the Inverse, and Properties of the InverseForget to transpose the cofactor matrix and the marks go. Learn the inverse in four steps.
11. Systems of Linear Equations: Cramer's Rule and the Inverse-Matrix MethodThe last part of a creative question is often “solve by Cramer's rule”. Swap the column, divide by D.

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