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Level 418

Systems & Matrices

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Solution of a System
A coordinate point that is a solution to all equations
Solve by Elimination
Method where one variable is removed from the equations so a different one can be solved.
a rectangular array of elements (or entries) set out by rows and columns
Element (Entry)
A single value value obtained from a matrix, in the form a₍ij₎, where i is the column number and j is the row number.
square matrix
the same number of elements in the rows and columns.
Matrix Addition
If A and B are both matrices of order m × n,
Matrix Subtraction
If A and B are both matrices of order m × n,
matrix multiplication
-can be multiplied if the # of A columns = # of B rows
Inverse of a Square Matrix
For any m × n matrix A = [a₍ij₎], the matrix B such that AB = BA = I₍n₎
Inverse of a 2 × 2 Matrix
If ad - bc ≠ 0, then
Determinant of a Square Matrix
For a n × n matrix A, where n > 2, the sum of the entries in any row or column multiplied by their respective cofactors.
Inverses of n × n Matrices
An n × n matrix has an inverse if and only if set A ≠ 0
Commutative Property
3 + 2 = 2 + 3
Associative Property
(1 + 2) + 3 = 1 + (2 + 3)
Identity Property
the sum of any number and zero is the original number
Inverse Property
The sum of a number and its opposite is 0.
distributive property
Multiplying a sum by a number is the same as multiplying each term by the number and then adding (or subtracting ) the products.
Equivalent Systems
Both systems have the same solution.
Gaussian Elimination
Method of solving systems of equations using the following rules:
Row Echelon Form of a Matrix
A system is in such if:
Partial Fraction Decomposition
For any function f(x) divided by the function d(x), where d(x) has n factors, represented by m,