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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
- Find the transpose of a matrix.
- Is the matrix symmetric?
- Find the inverse of a matrix.
- Is `A` orthogonal?
- Add two matrices.
- Multiply a matrix times a column vector.
- Multiply a row vector times a matrix.
- Multiply a matrix times a matrix.
- What size is AB if A is mxn and B is nxp?
- Compute a matrix product column by column.
- Compute a matrix product row by row.
- Compute a matrix product entry by entry.
- Compute a matrix product as a sum of rank one matrices.
- Use the LU factorization of a matrix.
- Find the LU factorization of a matrix.
- Find the permuted LU factorization of a matrix.
- Is a vector in Col(`A`) and/or Nul(`A`)?
- Find a vector in Col(`A`) and/or Nul(`A`)
- Find bases for Col(`A`) and Nul(`A`)
- Find bases for Col(`A`), Nul(`A`), Col(`A^T`) and Nul(`A^T`)
- Find the rank of a matrix.
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