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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.
■(1&2&3@1&1&1@-1&1&2) {█(x@y@z)┤ = {█(1@12@2)┤

Find the determinant of the given matrix.

■(1&0&6 -1@-6&0&2 4@3&0&6 -2 )
3 4 -3 3

Find the determinant of the given matrix.

■(-1&2&-2@5&-1&-5@5&4&4)

Determine whether the matrix is invertible by finding the determinant of the matrix.
[■(1/6&-1/7@ -49&42)]

Find the inverse of the matrix.
A = 3 0
-1 -4

Perform the indicated operation, if possible.
[■(-1&0@4&3)] - [■(-1&4@3&1)]

Decide whether or not matrix B is the inverse of matrix A.
A = [■(-5&1@ -7&1)]

B= [■(1/2&-1/2@7/2&-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 × 1, B is 1 × 4.

Given matrices A and B, find the indicated matrix if possible.
A = [■(-2&0@1&-5)] B = [■(- 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.
+ ■(3&-4@-7&-5@5&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

Attachments

Solution Preview

The solution file is attached.

Write the matrix equation as a system of equations and solve the system.
■(1&2&3@1&1&1@-1&1&2) {█(x@y@z)┤ = {█(1@12@2)┤

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)  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.

■(1&0&6 -1@-6&0&2 4@3&0&6 -2 )
...

Solution Summary

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

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