Linear Algebra Chapter 1 Questions and Answers.
Linear Equation Correct Answer: describes a first-order line in Rn equations of the form
... [Show More] a1x1+a2x2+...+anxn=C, where a1...an are R and x1...xn are variables
System of Linear Equations Correct Answer: a collection of 1+ linear equations to be solved simultaneously
Solution Correct Answer: a set of real numbers s1...sn such that each equation holds if we set x1=s1... xn=sn
Solution Set Correct Answer: a set of all solutions in a system
Consistent System Correct Answer: at least one solution exists
Inconsistent System Correct Answer: no solutions exist
Equivalent Systems Correct Answer: two systems that have the same solution set
How to solve a basic system Correct Answer: use interchanging, scaling, and replacement to isolate the variable and then plug into other variables
Interchange Correct Answer: reorder equations
Scaling Correct Answer: multiply each equation by a constant
Replacement Correct Answer: replacing one equation with itself and a multiple of another
Matrix (m x n) Correct Answer: a rectangular array of numbers with m rows and n columns
Augmented Matrix Correct Answer: a matrix that includes a set of constant solutions (numbers without variables)
Solving a matrix Correct Answer: try to make each pivot equal to one, with each pivot being the only number in its column, and the only other number in the row being the rightmost number
Echelon Form Correct Answer: 1. all 0 rows at bottom of the matrix
2. each leading nonzero entry in a row to the right of the leading nonzero entry in the previous row
3. all entries in the column beneath a leading nonzero entry are 0's
Reduced Echelon Form Correct Answer: All the requirements for Echelon Form 1. all 0 rows at the bottom of the matrix
2. each leading nonzero entry in a row to the right of the leading nonzero entry in the previous row
3. all entries in the column beneath a leading nonzero entry are 0's
Plus
4. each leading nonzero entry is 1
5. each leading nonzero entry is the only nonzero entry in its column
Pivot Correct Answer: leading nonzero entry in an echelon matrix [Show Less]