Calculus 3 : Matrices

Example Questions

Example Question #121 : Matrices

Perform the following matrix operation:      Explanation:

To perform the matrix operation, you must follow the formula .

Using the values we have, this becomes which simplified is Example Question #122 : Matrices

Find the determinant of the 3x3 matrix:      Explanation:

The formula for the determinant is as follows: ,

where .

Using the matrix in the problem, we get Example Question #123 : Matrices What is ?    Explanation:

To find , we write the rows of as columns.

Hence, Example Question #124 : Matrices

Find the determinant of the 3x3 matrix      Explanation:

The formula for the determinant of a 3x3 matrix is . Using the matrix in the problem statement, we get Example Question #125 : Matrices

Evaluate the determinant of the matrix.      Explanation:

The determinant of the matrix is defined as For the matrix in this problem the determinant is   Example Question #126 : Matrices

Find the determinant of the matrix:      Explanation:

To find the determinant of the matrix, we multiply across, from top left to bottom right, and then subtract the product of multiplying across from top right to bottom left:  Example Question #127 : Matrices

Find the determinant of the 2x2 matrix      Explanation:

The formula for the determinant of a 2x2 matrix is . Using the matrix from the problem statement, we get Example Question #128 : Matrices

Find the determinant of the 2x2 matrix      Explanation:

The formula foe the determinant of a 2x2 matrix is . Using the matrix from the problem statement, we get Example Question #129 : Matrices

Find the determinant of the given matrix:      Explanation:

The determinant of the matrix is found by multiplying from top left to bottom right, and then subtracting the product from top right to bottom left (for example, the determinant of ) Example Question #130 : Matrices

Find the determinant of the 2x2 matrix      To find the determinant of a 2x2 matrix we use the formula for the determinant, which is . Plugging in the values from the problem statement, we find that the determinant of the matrix is  