1. Consider the matrix -3 1. -2 3 1 -1 6 1 (a) Find a basis for Im(A). Be sure to show your work. (b) Fill in the blanks below The image of A is a in (line/plane/other space) (R" for what n)

Q: Prove or disprove. a) det(4+ B) = det(4) + det(B) b) det(ABTA-) = det B

A: To prove or disprove : det(A+B)=det(A)+det(B)

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A: The given equation is.    95=-4(m-3)2-5                                     ⇒100=-4(m-3)2  ....(1)  ...

Q: c) Find a subset of S that is a basis for W. d) Express v= as a linear combination of the basis obta...

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Q: y(x³ – y)dx – x(x³ + y)dy = 0 | - Use the exact differentials to solve the differential equation. Ch...

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Q: 3) a) i) Calculate the simple interest earned if a deposit of  $ 200,000 is left for 12 years at an ...

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Q: Use the Comparison Test to determine if the series 5n – cos 2n n + n2 + 1 T=1 converges or diverges.

A: Comparison  Test :    If ∑n=1∞ an and ∑n=1∞ bn be the two positive term series and an≤ K.bn for all ...

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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

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Q: subgroup of order p and only one subgroup of order q, prove that G is cyclic. (5) Show that in a gro...

A: Introduction: The order of a group is the number of elements in the group. If the number of elements...

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Q: Let p and q be propositions. Then p →1 19 A(p → q)] is a contradiction contingency tautology

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Q: 1. Apply transformations Sketch the transformation of the rectangle with vertices -2 -2 3 3] -1 -1 u...

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Q: Consider the divisibility partial order on N. Find a, b E N so that the interval poset a, b| has hei...

A: To find- Consider the divisibility partial order | on ℕ. Find a, b ∈ ℕ so that the interval poset a,...

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0, 1...

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Q: [1-4 7 -5] and let A = 0 1 -4 3 L2-6 6 –4] Let b = Is b in the range of the linear transformation X ...

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Q: (c) Find the chromatic polynomial of the graph in Figure 4. Figure 4:

A: Graph theory

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Q: Sketch the transformation of the rectangle with vertices -2 -2 3 3] -1 -1 1 under Mị = M2 1/2 M3 M4 ...

A: This is a problem of linear transformation.

Q: a az 3. In R, let Wbe the subset of all vectors v = that satisfy a, -a, = a, – a,. az a4 a) Show tha...

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Q: Find r(t). 1 (s + 8)3 f(t) =

A: L { xn} = n!sn+1L-1 n!sn+1 = xnL-1 1s2+1 = x2L-11s3 = x2Also L{ eat f(t) }= F (s-a)L{ e-8t  t} = 1(s...

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Q: 11. A water tank is to be constructed with a square base and open top, and is to hold 64 cuble yards...

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Q: Which among the following statements is true? * Every conditional statement is logically equivalent ...

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Q: Solve the initial value problem using the Laplace transform. y' = 9y + 6, y(0) = 1 y(t)

A: We solve the given IVP  y'=9y+6.....(1) y(0)=1 by using Laplace transform.  

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Q: Let Mıs(IR) = {A/A and 15th order square matrix with real elements} and consider the linear operator...

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Q: Give an example of a function f which is integrable on (0,1] such that f(z) >0 for all (a) IE (0,1] ...

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Q: g(x) is integrable on [a, b), and S(r)dr Ja Ja | 9(1)dr.

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Q: (c) Find the chromatic polynomial of the graph in Figure 4. Figure 4:

A: Chromatic number of the graph

Q: Evaluate| [(A + B) C]T Dª | 1 A = B = 0 0 0 0 b/5 1 e C=2 21 D = e * ON xO - NO O O ON O O O3 O*NO-3...

A:   The main objective is to calculate the det of 

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Q: Determine the solution of the initial value problem 1. 5y" + y' = -6x, y(0) = 0, y'(0) = -10

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Q: Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the d...

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Q: Show is a contour plot for a function z = 3 В A (a) Is fy positive, negative, or zero at A? (b) Is f...

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