Practice Test B

  1. Give the order of the matrix and the value of the designated entries of the matrix.

    A=[030−10614−57−78−159−613−20.4114−30]a34

    1. Order: 5×4; a34=6

    2. Order: 4×5; a34=11

    3. Order: 20; a34=−4

    4. Order: 4×5; a34=13

  2. Write an augmented matrix for the following system of equations.

    {8x+4y+5z=10−2x+3y+6z=−9−2x8y+6z=4

    1. [845−236−286]

    2. [10548−963−2468−2]

    3. [8−2−210438−95664]

    4. [84510−236−9−2864]

  3. Write the system of linear equations represented by the following augmented matrix.

    [−170−6206508−84]

    Use x, y, and z for the variables.

    1. {x+7y+z=−62x+6z=58y+8z=4

    2. {−x+7y+z=−62x+6y=58x−8y=4

    3. {−x+7y+z=−62x+y+6z=5x+8y−8z=4

    4. {−x+7y=−62x+6z−58y−8z=4

  4. Find values for the variables so that the matrices

    [x+3y+473]and[927z]

    are equal.

    1. x=−6; y=2; z=3

    2. x=6; y=9; z=3

    3. x=6; y=−2; z=3

    4. x=9; y=2; z=3

  5. Find the value of z in the following system.

    {2x+y=152y+z=252z+x=26

    1. 4

    2. 9

    3. 11

    4. 12

  6. Find the value of 4x+3y+z in the following system.

    {2x+y=17y+2z=15x+z=9

    1. 41

    2. 43

    3. 55

    4. 45

  7. Let A=[−14048−4] and B=[7217422]. Find A−B.

    1. [12706−2]

    2. [3−370−66]

    3. [−82−1706−6]

    4. [1578100]

In Problems 8 and 9, find the product AB if possible.

  1. A=[−829], B=[30−3]

    1. [−240−27]

    2. [−51]

    3. [210]

    4. [−240−27]

  2. A=[3−2104−2], B=[50−21]

    1. AB is not defined.

    2. [15−105−68−4]

    3. [15−6−1085−4]

    4. [15004]

For Problems 10–13, let

A=[21−3−521], B=[−3724], and C=[5410].

  1. Find 2A.

    1. [112−32−52112]

    2. [42−6−1042]

    3. [43−1−343]

    4. [0−1−5−70−1]

  2. Find A+BA.

    1. [2−410−545]

    2. [4−26−1042]

    3. [−391213−2112−1]

    4. [−4117−2−16610]

  3. Find C2.

    1. [10820]

    2. [41551]

    3. [292054]

    4. [0415]

  4. Find C−1.

    1. [−541140]

    2. [0114−54]

    3. [14−5401]

    4. [0−1−14−54]

  5. Find the inverse of the following matrix.

    A=[1002103−41]

    1. [100−210341]

    2. [100−210−831]

    3. [1−2−11014001]

    4. [100−210−1141]

  6. Write the linear system as a matrix equation

    {4x+2y=15−2x+4y=9

    in the form AX=B, where A is the coefficient matrix and B is the constant matrix.

    1. [42−24][xy]=[159]

    2. [424−2][xy]=[159]

    3. [1529−2][xy]=[44]

    4. [4−224][xy]=[159]

  7. Write the matrix equation

    [−39−8−4][xy]=[−4−5]

    as a system of linear equations.

    1. {−3x+9y=−4−8x−4y=−5

    2. {−3x+9y=−4−4x−8y=−5

    3. {9x−3y=−4−8x−4y=−5

    4. {−3x+9y=4−8x−4y=5

  8. Let A=[−2−31−53−2] and B=[−1−2−1101].

    Solve the matrix equation A−3X=−5B for X.

    1. X=[−52−92−1−13212]

    2. X=[−73−133−43011]

    3. X=[−132−1−52−92−1]

    4. X=[−131383−2033−113]

In Problems 18 and 19, evaluate the determinant.

  1. |−85−4−1|

    1. −28

    2. −44

    3. −12

    4. 28

  2. |23−230−3−30−5|

    1. −72

    2. 18

    3. 72

    4. −18

  3. Solve the system of equations

    {x+y+z=−6x−y+3z=−222x+y+z=−10

    by using Cramer’s Rule.

    1. ∅

    2. {(−4, 3, −5)}

    3. {(−5, −4, 3)}

    4. {(−5, 3, −4)}

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