# Advanced Algebra MATH 003 (TIP Reviewer)

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

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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