Advanced Algebra MATH 003 (TIP Reviewer)

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  • 7/23/2019 Advanced Algebra MATH 003 (TIP Reviewer)

    1/1

    Matrix: rectangular array of numbers

    Elements: aij where i (row) and a j (column)

    Matrix dimension: m (row) by n (column)

    *Zero matrix - matrix having zeroes for all its members. Also called additive identity..

    You can only add if they have the same dimensions for both row and columns! (2x3 + 2x3)b.

    Add each elements correspondingly.c.

    Addition: Add the corresponding elements of matrices have the same dimension.

    Additive inverse of a matrix: replace each element by additive inverse.

    You can only subtract if they have the same dimensions for both row and columns (2x3 + 2x3).

    Subtraction: Subtract the corresponding elements..

    Scalar product of a real number (K) - multiply each element by the number K. K times each element!.

    Multiplication of 2 matrices: Multiply the element in row i of the first matrix to the column j of the second matrix.

    The product of an m x n matrix and n x p matrix is an m x p matrix..

    Before multiplying, check first if they can be multiplied. Kailangang pareho yung means: column ng first matrix =

    second matrix.

    d.

    A (3 x 2) * B (2 X 3) = C (3 X 3).

    Multiplication:.

    Operation of Matrix

    Determinants:

    *Square Matrix: a matrix with the same number of rows and columns (Ex: 2x2, 3x3, 4x4)

    Cramer's Rule:

    The system of 2 equations in 2 variables:

    Has a solution given by:

    *Kung ano yung hinahanap na variable, palitan ng values ng C. Don't forget to divide the x, y and z by d

    If D = 0, and the determinants of the numerators are also 0 , then the system of the equation is dependent. Equation 1 a

    just the same line.

    1.

    If D = 0, and at least one of the other determinants is non-zero, then the system is inconsistent. Equation 1 and 2 form p

    lines.

    2.

    If D = 0, then one of the situation occurs:

    Midterm:

    Thursday, August 14, 2014 10:54 AM

    Advanced Algebra Page 1

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