Math 2890 - Sample Chapter 2 Problems

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Chapter 2

2.1      Matrix Operations
2.2      The Inverse of a Matrix
2.3      Characterizations of Invertible Matrices
2.4      Partitioned Matrices
2.5      Matrix Factorizations
         Wedderburn Rank Reduction
2.7      Applications to Computer Graphics
2.8      Subspaces of R^n
2.9      Dimension and Rank

1. Find the transpose of a matrix.
2. Is the matrix symmetric?
3. Find the inverse of a matrix.
4. Is `A` orthogonal?

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5. Add two matrices.
6. Multiply a matrix times a column vector.
7. Multiply a row vector times a matrix.
8. Multiply a matrix times a matrix.

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9. What size is AB if A is mxn and B is nxp?
10. Compute a matrix product column by column.
11. Compute a matrix product row by row.
12. Compute a matrix product entry by entry.
13. Compute a matrix product as a sum of rank one matrices.

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14. Use the LU factorization of a matrix.
15. Find the LU factorization of a matrix.
16. Find the permuted LU factorization of a matrix.

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17. Is a vector in Col(`A`) and/or Nul(`A`)?
18. Find a vector in Col(`A`) and/or Nul(`A`)
19. Find bases for Col(`A`) and Nul(`A`)
20. Find bases for Col(`A`), Nul(`A`), Col(`A^T`) and Nul(`A^T`)
21. Find the rank of a matrix.

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