Question

Let A = [a_{ij}] be a square matrix. a. If A has a zero row (column), then det(A) = 0. b. If B is obtained by interchanging two rows (columns) of A, then det(B) = -det(A). c. If A has two identical rows (columns), then det(A) = 0. d. If B is obtained by multiplying a row (column) of A by k, then det B = k det(A). e. If A, B, and C are identical except that the ith row (column) of C is the sum of the ith rows (columns) of A and B, then det(C) = det(A) + det(B). f. If B is obtained by adding a multiple of one row (column) of A to another row (column), then det(B) = det(A). Evaluate the given determinant using elementary row and/or column operations and the theorem above to reduce the matrix to row echelon form. | 1 -1 0 3 | | 2 7 2 6 | | 0 1 0 0 | | 1 6 2 1 |

          Let A = [a_{ij}] be a square matrix.
a. If A has a zero row (column), then det(A) = 0.
b. If B is obtained by interchanging two rows (columns) of A, then det(B) = -det(A).
c. If A has two identical rows (columns), then det(A) = 0.
d. If B is obtained by multiplying a row (column) of A by k, then det B = k det(A).
e. If A, B, and C are identical except that the ith row (column) of C is the sum of the ith rows (columns) of A and B, then det(C) = det(A) + det(B).
f. If B is obtained by adding a multiple of one row (column) of A to another row (column), then det(B) = det(A).
Evaluate the given determinant using elementary row and/or column operations and the theorem above to reduce the matrix to row echelon form.
| 1 -1 0 3 |
| 2 7 2 6 |
| 0 1 0 0 |
| 1 6 2 1 |

Let A = [aij] be a square matrix.
a. If A has a zero row (column), then det(A) = 0.
b. If B is obtained by interchanging two rows (columns) of A, then det(B) = -det(A).
c. If A has two identical rows (columns), then det(A) = 0.
d. If B is obtained by multiplying a row (column) of A by k, then det B = k det(A).
e. If A, B, and C are identical except that the ith row (column) of C is the sum of the ith rows (columns) of A and B, then det(C) = det(A) + det(B).
f. If B is obtained by adding a multiple of one row (column) of A to another row (column), then det(B) = det(A).
Evaluate the given determinant using elementary row and/or column operations and the theorem above to reduce the matrix to row echelon form.
| 1 -1 0 3 |
| 2 7 2 6 |
| 0 1 0 0 |
| 1 6 2 1 |

Added by Brandy R.

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