# Determinants, Matrices, Inverse, Linear equations

Practice problems on determinants and matrices. All questions can be found in the attached file.

Write the matrix equation as a system of equations and solve the system.

â– (1&2&[email protected]&1&[email protected]&1&2) {â–ˆ([email protected]@z)â”¤ = {â–ˆ([email protected]@2)â”¤

Find the determinant of the given matrix.

â– (1&0&6 [email protected]&0&2 [email protected]&0&6 -2 )

3 4 -3 3

Find the determinant of the given matrix.

â– (-1&2&[email protected]&-1&[email protected]&4&4)

Determine whether the matrix is invertible by finding the determinant of the matrix.

[â– (1/6&-1/[email protected] -49&42)]

Find the inverse of the matrix.

A = 3 0

-1 -4

Perform the indicated operation, if possible.

[â– (-1&[email protected]&3)] - [â– (-1&[email protected]&1)]

Decide whether or not matrix B is the inverse of matrix A.

A = [â– (-5&[email protected] -7&1)]

B= [â– (1/2&-1/[email protected]/2&-5/2)]

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist.

A is 4 Ã— 1, B is 1 Ã— 4.

Given matrices A and B, find the indicated matrix if possible.

A = [â– (-2&[email protected]&-5)] B = [â– (- 3&@ -2& )]Find AB.

Write the augmented matrix for the system.

9x + 2y + 9z = 8

8x + 5y + 2z = 26

9x + 2y + 3z = 14

Find the sum, if possible.

+ â– (3&[email protected]&[email protected]&8)

Find the minor for the element in the first row and second column of the given matrix.

11 -11 20

-3 19 16

4 6 -8

https://brainmass.com/math/linear-algebra/determinants-matrices-inverse-linear-equations-177606

#### Solution Preview

The solution file is attached.

Write the matrix equation as a system of equations and solve the system.

â– (1&2&[email protected]&1&[email protected]&1&2) {â–ˆ([email protected]@z)â”¤ = {â–ˆ([email protected]@2)â”¤

The system is:

x + 2y + 3z = 1 --- (1)

x + y + z = 12 --- (2)

-x + y + 2z = 2 --- (3)

Adding (2) and (3) we get 2y + 3z = 14 --- (4)

Subtracting (2) from (1) we get y + 2z = -11 --- (5)

(4) - 2 * (5) ïƒž 3z - 4z = 14 - 2(-11)

-z = 36

z = -36

From (5) y = -11 - 2z = -11 - 2(-36) = 61

From (2) x = 12 - y - z = 12 - 61 + 36 = -13

The solution is x = -13, y = 61, z = -36

Find the determinant of the given matrix.

â– (1&0&6 [email protected]&0&2 [email protected]&0&6 -2 )

...

#### Solution Summary

Practice problems on determinants, matrices, inverse, augmented matrices, system of linear equations solved.