Question

Find the determinants in exercises 5-10 by row reduction to echelon form.

a. Matrix multiplication
b. Cramer's rule
c. Gaussian elimination
d. Laplace expansion

Answer 1

To find the determinants in exercises 5-10, you can use matrix multiplication, Cramer's rule, Gaussian elimination, or Laplace expansion.

Step-by-step explanation:

The determinants can be found in exercises 5-10 by performing various operations:

1. Matrix multiplication: Multiply the elements of each row by the corresponding cofactors and then sum the products to find the determinant.
2. Cramer's rule: Use the formula involving determinants of matrices formed by substituting the column of constants into the original matrix.
3. Gaussian elimination: Use row operations to transform the matrix into echelon form, and then multiply the diagonal elements to find the determinant.
4. Laplace expansion: Select a row or column, multiply each element by the determinant of the minor matrix formed by removing that row/column, and alternate the signs before summing the products.