Final (Everything)

Question 1

Linear Equation

Answer 1

An equation that can be written in the form
a1x1 + a2x2 +… anxn = b

Question 2

Coefficients

Answer 2

a1, a2, … an
Real or complex numbers

Question 3

Is the following a linear equation?
4x1 - 5x2 +2 = x1

Answer 3

Yes

Question 4

Is the following a linear equation?
x2 = 2(sqrt(6)-x1)+x3

Answer 4

Yes

Question 5

Is the following equation linear?
4x1-5x2= x1x2

Answer 5

No

Question 6

A system of linear equations or linear system

Answer 6

A collection of one or more linear equations involving the same variables

Question 7

Solution

Answer 7

A list of numbers that make each equation a true statement when the values s1, s2, sn are substituted for x1, x2, xn respectively

Question 8

Solution set

Answer 8

The set of all possible solutions

Question 9

Equivalent

Answer 9

Two linear systems are equivalent if they have the same solution set.

Question 10

What are the solution options for linear systems

Answer 10

No solution, one solution or infinity many solutions

Question 11

Consistent

Answer 11

If it has either one solution or infinitely many solutions

Question 12

Inconsistent

Answer 12

Has no solution

Question 13

Diagonalizable

Answer 13

A square matrix A is said to be diagonalizable if A is similar to a diagonal matrix that is if A =PDP^-1 for some invertible matrix P and some diagonal matrix D