College Algebra- Matrices and Sequences
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Matrix Outcomes
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Unique Solution, No Solution, Infinite Solutions
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Unique Solution
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Indicates the system is consistent.
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No Solution
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Indicates the system is inconsistent. In Gauss Jordan Elimination, if a zero appears on the left side and a non zero appear on the right side of the row, the system has no solution.
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Infinite Solutions
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Indicate the system is dependent. In Gauss Jordan Elimination, if a row becomes all zeros, the system has infinite solutions.
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Methods for solving Systems of Linear Equations
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Elimination, Substitution, Graphing, Gauss Jordan
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Matrix
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A rectangular array of elements enclosed in square brackets.
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Matrix size
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Rows * Columns
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Entering Matrix in the TI-84 Calculator
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2nd, x⁻¹ \"Matrix\"→ Edit 1: \"Enter\" Input size of the Matrix, \"Enter\", Input elements horizontally, 2nd, Mode \"Quit\".
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Using Row Ops
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\"Prgm\", Row Ops, \"Enter\", Select Matrix, Enter.
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Gauss Jordan Elimination, Getting 1's
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Getting 1's: Row Swap can only be performed on your first step. (Option 1 in Row Ops) Multiply row by the reciprocal. (Option 3 in Row Ops)
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Gauss Jordan Elimination, Getting 0's
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Getting 0's: Multiply by additive inverse. (Option 2 in Row Ops) Add rows, (Option 4 in Row Ops)
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Sequence
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A list of numbers in a well defined order. A sequence is a function whose domain is the set of all positive integers.
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Arithmetic Sequence
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A sequence in which any 2 consecutive terms differ by a constant amount, \"d\". An Arithmetic Sequence is a linear function whose domain is the set of positive integers.
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Arithmetic Specific Term Formula
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An= a₁+(n-1)d
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Arithmetic Partial Sum Formula
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Sn= n/2(a₁+an)
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Geometric Sequence
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A sequence in which any 2 consecutive terms differ by a constant ratio, \"r\". A Geometric Sequence is an exponential function whose domain is the set of all positive integers only when r>0.
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Geometric Specific Sum Formula
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An=a₁(r)ⁿ⁻¹
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Geometric Partial Sum Formula
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Sn=a₁* (1-rⁿ)/1-r, r≠0,1
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Infinite Sum
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S∞= a₁/1-r, only if |1|<1
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Summation Notation
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A short hand way to describe a partial sum.
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Factorial Notation
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Symbol is !. On the calculator: \"Math\" →PRB→4:! 4!= 1*2*3*4=24
