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Tutor profile: Brad M.

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Brad M.
Math Instructor and Tutor
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Questions

Subject: Linear Algebra

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Question:

Let A be a linear transfomation from $$\mathbb{R}^n $$ to $$\mathbb{R}^n $$. If $$ker(A)={0}$$, then A is injective

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Brad M.
Answer:

Proof: Let $$Ax_1=Ax_2$$; then $$Ax_1-Ax_2=0$$. This implies that $$A(x_1-x_2)=0$$. Since the kernel of A is just the zero vector, then $$x_1-x_2=0$$. Therefore we can conclude that $$x_1 = x_2$$ which means that A is injective.

Subject: Calculus

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Question:

Integrate $$1/(x^2+1)$$

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Brad M.
Answer:

$$arctan(x)+C$$

Subject: Differential Equations

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Question:

Find the general solution of the differential equation $$dy/dx = x^2 $$

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Brad M.
Answer:

$$x^3/3+C$$

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