Mark T.

Civil engineer from Cal Poly Pomona

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Linear Algebra

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Question:

x(1) − 2x(2) + 2x(3) = 5 x(1) − x(2) = −1 −x(1) + x(2) + x(3) = 5 Find Solutions to x(1), x(2), and x(3).

Mark T.

Answer:

create a matrix using the coefficients in front of each variable. 1 −2 2 5 1 −1 0 −1 −1 1 1 5 Reduce until you get to 1 0 0 1 0 1 0 2 0 0 1 4 x(1) = 1 x(2) = 2 x(3) = 4

Pre-Algebra

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Question:

Solve: (5 + 5n^3) − (1 − 3n^3)

Mark T.

Answer:

Distribute the - into the parenthesis so that you end up with +(-1+3n^3). Then combine like terms such as (5,1) and (3n^3, 5n^3) such that: (5-1) + (5n^3+3n^3) = (4 + 8n^3)

Calculus

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Question:

If f(x) and g(x) are differentiable functions such that f '(x) = 3 x and g '(x) = 2 x ^2 then the limit lim [(f(x) + g(x)) - (f(1) + g(1))] / (x - 1) as x approaches 1. is equal to

Mark T.

Answer:

The given limit is the definition of the derivative of f(x) + g(x) at x = 1. The derivative of the sum is equal to the sum of the derivatives. Hence the given limit is equal to f '(1) + g '(1) = 5.

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