Mathematics: Advanced Matrices Test

1) Find the determinant of the following matrix.

-47

47

23

-23

27

The given matrix is a 2x2 matrix. To find the determinant of a 2x2 matrix, we use the formula ad - bc. In this case, the determinant is (-47 * 27) - (47 * -23) = -1271 - (-1081) = -1271 + 1081 = -190. However, the answer given is 23, which is incorrect.

Explanation

The given matrix is a 2x2 matrix. To find the determinant of a 2x2 matrix, we use the formula ad - bc. In this case, the determinant is (-47 * 27) - (47 * -23) = -1271 - (-1081) = -1271 + 1081 = -190. However, the answer given is 23, which is incorrect.

2) To find the inverse of the following matrix, what would be the next step you would perform?

R1 --> R1+ (2)R2

R1 --> R1/(-2)

R2 --> R2/(-2)

R1 --> R1 + 2

The next step to find the inverse of the matrix would be to perform the operation R1 --> R1/(-2). This step involves dividing every element in the first row of the matrix by -2. This operation is necessary to manipulate the matrix and eventually obtain the inverse.

Explanation

The next step to find the inverse of the matrix would be to perform the operation R1 --> R1/(-2). This step involves dividing every element in the first row of the matrix by -2. This operation is necessary to manipulate the matrix and eventually obtain the inverse.

3) Find the inverse of the following matrix if it exists.

A

B

C

D

The inverse does not exist.

The given answer is correct because in order for a matrix to have an inverse, it must be a square matrix (i.e., have the same number of rows and columns) and have a non-zero determinant. However, the given matrix is not a square matrix, as it has 4 rows and 1 column. Therefore, it does not have an inverse.

Explanation

The given answer is correct because in order for a matrix to have an inverse, it must be a square matrix (i.e., have the same number of rows and columns) and have a non-zero determinant. However, the given matrix is not a square matrix, as it has 4 rows and 1 column. Therefore, it does not have an inverse.

4) To find the inverse of the following matrix, what would be the next step you would perform?

R1 --> R1/(-2)

R2 --> (4)R2 - (9)R1

R2 --> R2/(-9)

R2 --> R2 - (2)R1

The next step to find the inverse of the matrix would be to divide the second row (R2) by -9.

Explanation

The next step to find the inverse of the matrix would be to divide the second row (R2) by -9.

5) Find the inverse of the following matrix if it exists.

A

B

C

D

The inverse does not exist.

The given matrix is not a square matrix, which means it does not have the same number of rows and columns. In order for a matrix to have an inverse, it must be a square matrix. Since the given matrix is not a square matrix, it does not have an inverse.

Explanation

The given matrix is not a square matrix, which means it does not have the same number of rows and columns. In order for a matrix to have an inverse, it must be a square matrix. Since the given matrix is not a square matrix, it does not have an inverse.

6) Find the inverse of the following matrix if it exists.

A

B

C

D

The inverse does not exist.

not-available-via-ai

Explanation

not-available-via-ai

7) To find the inverse of the following matrix. What would your first step be? (Assume the inverse exists.)

R1 --> R1 + (4)R1

R2 --> R2/8

R1--> R1/-2

R2--> R2 +(4)R1

The given answer suggests that the first step to find the inverse of the matrix is to perform the operation R2 --> R2 +(4)R1. This means that we need to add 4 times the first row to the second row.

Explanation

The given answer suggests that the first step to find the inverse of the matrix is to perform the operation R2 --> R2 +(4)R1. This means that we need to add 4 times the first row to the second row.

8) Use matrices to solve the following system of equations.
-2x - 4y = 388x + 7y = -53

(-3, -11)

(8.8, 22.7)

(8.8, -22.7)

(41.56, -22.7)

(3, -11)

The answer (3, -11) is obtained by solving the system of equations using matrices. By setting up the coefficient matrix and the constant matrix, we can use matrix operations to find the values of x and y that satisfy both equations simultaneously. The resulting solution is (3, -11), which means that when x is 3 and y is -11, both equations are true.

Explanation

The answer (3, -11) is obtained by solving the system of equations using matrices. By setting up the coefficient matrix and the constant matrix, we can use matrix operations to find the values of x and y that satisfy both equations simultaneously. The resulting solution is (3, -11), which means that when x is 3 and y is -11, both equations are true.