Linear Algebra Chapter 1

Linear Algebra Chapter 1 Questions and Answers. Linear Equation Correct Answer: describes a first-order line in Rn equations of the form 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)