Use matrix operations to solve the following systems of linear equations. Use comments to explain which value is x1, x2, etc 3x1-10 x2- 5x3+30x4 = -1
4x1+7x2+ 5x3- 3x4=0
x2+ x3-3x4 =1
x1-2x2-10x3+6x4 = -1

x⁴ = -0.955939

x³ = 0.206897

x² = -2.07471

x = 2.65517

Step-by-step explanation:

Step 1: Rewrite equations in standard form

30x⁴ - 5x³ - 10x² + 3x = -1

-3x⁴ + 5x³ + 7x² + 4x = 0

-3x⁴ + x³ + x² = 1

6x⁴ - 10x³ - 2x² + x = -1

Step 2: Write in matrix form

Top Row: [30 -5 -10 3 | -1]

2nd Row: [-3 5 7 4 | 0]

3rd Row: [-3 1 1 0 0 | 1]

Bottom Row: [6 -10 -2 1 | -1]

Step 3: Plug in calc with RREF function

Top Row: [1 0 0 0 | -499/522]

2nd Row: [0 1 0 0 | 6/29]

3rd Row: [0 0 1 0 | -361/174]

4th Row: [0 0 0 1 | 77/29]

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.