Tim S.

Tutor for many years

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Linear Algebra

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Question:

Find the inner product of the vector $$(1, 2, 5)$$ with $$(5, 2, 7)$$.

Tim S.

Answer:

To find the inner product we multiply the corresponding components of each vector and then sum them together. Thus, the inner product is $$1*5+2*2+5*7=44$$.

Pre-Calculus

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Question:

Factor the polynomial $$x^2-5x+6$$ and find its roots.

Tim S.

Answer:

We can factor the polynomial as $$(x-2)(x-3)$$. To find the roots we set each factor equal to $$0$$. So $$x-2=0$$ and $$x-3=0$$. Solving these two equations we find the roots are $$x=2$$ and $$x=3$$.

Calculus

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Question:

Find the derivative of the function $$f(x) = x^2$$.

Tim S.

Answer:

To find the derivative of $$x^2$$ we use the power rule. The power rule states that if $$f(x) = x^n$$ then the derivative is $$f'(x)=nx^{n-1}$$. Thus using the power rule if $$f(x)=x^2$$ then $$f'(x)=2x$$.

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