applied linear algebra

1.(2 pts) How do we know if an equation is linear by just looking at the equation?

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A hyperplane has the equation: z = s1x1 + s2x2 + s3x3 + … + s0 ‘ si represent the slopes of the plane in the respective xi-directions, while s0 represents the z-intercept.

2.(4 pts) True/False: Based on the above, all planes, z, are linear.

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3.(3 pts) True/False: Let ; z1 is linear.

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For the next 2 questions, consider this simple equation: y = mx + b

4.(3 pts) List below just one of the two variables in the equation.

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5.(4 pts) Let’s say that we have two boundary conditions for the above generic equation; this means that the other two elements in y, look like variables, but are not variables; rather, these are called “what”?

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Consider this polynomial for the next 4 questions: f(xi) = c0 + c1x1 + c2x2 + ××× + c10x10

6.(3 pts) How many distinct variables are there in f(xi)? Just type in a number

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7.(4 pts) How many distinct unknowns are there in f(xi)? Just type in a number

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8.(5 pts) Regarding your answer to #8, how many unique boundary conditions are required to define the values of f(xi)’s unknowns? Just type in a number

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9.(4 pts) What is the ‘value’ of the y-intercept for f(xi), if it can be defined; if it cannot be defined, then type in CBD.

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