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MTH355 ~ Chp 3 Terms
Linear Algebra Terms ~ Chp 3, Test 3
| Question | Answer |
|---|---|
| Properties of Determinants: The elements in a row/column of matrix A are multiplied by c. What is B (the resulting matrix)? | B = cA |
| Properties of Determinants: Two rows/columns of matrix A are interchanged. What is B (the resulting matrix)? | B = -A |
| Properties of Determinants: In matrix A a multiple of one row/column is added to another row/column. What is B (the resulting matrix)? | B = A |
| Definition: Determinant of a square matrix | The sum of the products of the elements of a row or column within a matrix and their cofactors. A real number associated with every square matrix. |
| Definition: Minor (of an Element) | The minor of element a(ij) is denoted M(ij) and is the determinant of the matrix that remains after deleting row i and column j of matrix A. |
| Definition: Cofactor (of an Element) | The cofactor of a(ij) is denoted C(ij) and is given by C(in) = (-1)^(i+j)*M(ij) |
| Definition: Determinantal Equation | A determinant that is expanded to yield an equation. |
| Definition: Singular Matrix | A square matrix A is said to be singular if A = 0. |
| Definition: Nonsingular Matrix | A square matrix A is nonsingular if A /= 0. |
| Theorem for Singular Matrices: Let A be a square matrix. A is singular if | 1) All the elements of a row/column are 02) Two rows/columns are equal3) Two rows/columns are proportional |
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sunrise016
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