Mathematics: Advanced Matrices Test

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Mathematics: Advanced Matrices Test - Quiz

Are you familiar with mathematics advanced matrices? Would you like to try this quiz? Matrices provide an example for researching the field properties that are often taken for granted as they work with real numbers: the properties of closure, classify, inverse, associativity, and distributivity. Matrices have a close connection with vectors which can be useful tools in analysis. If you want to put your knowledge to the test, this quiz can help.


Questions and Answers
  • 1. 

    Find the determinant of the following matrix.

    • A.

      -47

    • B.

      47

    • C.

      23

    • D.

      -23

    • E.

      27

    Correct Answer
    C. 23
    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.

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  • 2. 

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

    • A.

      R1 --> R1 + (4)R1

    • B.

      R2 --> R2/8

    • C.

      R1--> R1/-2

    • D.

      R2--> R2 +(4)R1

    Correct Answer
    D. R2--> R2 +(4)R1
    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.

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  • 3. 

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

    • A.

      R1 --> R1/(-2)

    • B.

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

    • C.

      R2 --> R2/(-9)

    • D.

      R2 --> R2 - (2)R1

    Correct Answer
    C. R2 --> R2/(-9)
    Explanation
    The next step to find the inverse of the matrix would be to divide the second row (R2) by -9.

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  • 4. 

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

    • A.

      R1 --> R1 + (4)R2

    • B.

      R1 --> R1/(-2)

    • C.

      R1 --> R1 + (3)R2

    • D.

      R2 --> (4)R2 +R1

    Correct Answer
    A. R1 --> R1 + (4)R2
    Explanation
    The next step to find the inverse of the matrix would be to perform the row operation R1 --> R1 + (4)R2.

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  • 5. 

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

    • A.

      R1 --> R1+ (2)R2

    • B.

      R1 --> R1/(-2)

    • C.

      R2 --> R2/(-2)

    • D.

      R1 --> R1 + 2

    Correct Answer
    B. R1 --> R1/(-2)
    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.

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  • 6. 

    Which of the following is the correct inverse  of the following matrix?

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    C. C
  • 7. 

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

    • A.

      (-3, -11)

    • B.

      (8.8, 22.7)

    • C.

      (8.8, -22.7)

    • D.

      (41.56, -22.7)

    • E.

      (3, -11)

    Correct Answer
    E. (3, -11)
    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.

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  • 8. 

    Find the inverse of the following matrix if it exists.

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    • E.

      The inverse does not exist.

    Correct Answer
    B. B
    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.

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  • 9. 

    Find the inverse of the following matrix if it exists.

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    • E.

      The inverse does not exist.

    Correct Answer
    E. The inverse does not exist.
    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.

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  • 10. 

    Find the inverse of the following matrix if it exists.

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    • E.

      The inverse does not exist.

    Correct Answer
    D. D

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  • Current Version
  • Mar 19, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Dec 06, 2009
    Quiz Created by
    Acapretto
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