A basis for the null space of the Matrix 1 2 3 A 2 4 6 is - 1 a. O b. O C. 00 { { { - 3 0 |} 1 2 0 1 2 0 3 0} 1 3 6} 1

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A: We will find out the required value.

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A: r(t)=(e2t, 2e2t , 2e6t)Find r'(t)Find T(t)

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A: We have to find the tangent line at the point .

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Q: Let f : R → R and ECR. Prove f is continuous iff f-¹(E) is closed whenever ECR is closed.

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A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 4. In the usual topology again, is locally compact? 5. Deduce. {(0, 0)} U {(x, y) = R²; x >0}

A: The given set is, .Locally compactness means that each point in the set has a compact neighborhood.

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A: We will find the expected payoffs.

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Q: S ASK YOUR TEACHER Use the properties of logarithms to write the log_(3)(x+8)+(1)/(5

A: The given logarithm

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Q: exponential functio

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Q: 7. Consider the boundary value problem x" + x = 0, x(0) = 0, x(π) = 0. Then A=4 is an eigenvalue for…

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A: Using basic formulas in trignometry we solve this problem.

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Q: For each of the following pairs of functions f,g: NR, state with a brief justification whether f(x)…

A: The Definitions: if there exist positive constants c and k such thatThis means that g(x) is an…