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    Determinants, Matrices, Inverse, Linear equations

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    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&[email protected]&1&[email protected]&1&2) {█([email protected]@z)┤ = {█([email protected]@2)┤

    Find the determinant of the given matrix.

    ■(1&0&6 [email protected]&0&2 [email protected]&0&6 -2 )
    3 4 -3 3

    Find the determinant of the given matrix.

    ■(-1&2&[email protected]&-1&[email protected]&4&4)

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

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

    Perform the indicated operation, if possible.
    [■(-1&[email protected]&3)] - [■(-1&[email protected]&1)]

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

    B= [■(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 × 1, B is 1 × 4.

    Given matrices A and B, find the indicated matrix if possible.
    A = [■(-2&[email protected]&-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&[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

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

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    The solution file is attached.

    Write the matrix equation as a system of equations and solve the system.
    ■(1&2&[email protected]&1&[email protected]&1&2) {█([email protected]@z)┤ = {█([email protected]@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 [email protected]&0&2 [email protected]&0&6 -2 )
    ...

    Solution Summary

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

    $2.49

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