If V = W1 e ... Wk, then there exist k linear operators E,, .., E, On V such (1) each E, is a projection (E = E?); (ii) E;E; = 0, if i # j; (iii) I = E1 + .. + Exi (iv) the range of E; is W; Conversely, if E;,..., E, are k linear operators on V which satisfy conditions ), (ii), and (iii), and if we let W, be the range of E,, then V = W, e . Wk. i.... %3D

Q: 7. What function would produce a graph that is the mirror image of the function y = 3.10*? a) y = 3x…

A: The mirror image is obtained by replacing with 2:

Q: With f = {(0,6), (1,3), (4,7), (5,8)} and g = {(-1, 2), (1, 4) , (2,3), (4,8)) Determines: A) f +…

A: Given f = {(0,6), (1,3), (4,7), (5,8)} and g = {(-1, 2), (1, 4) , (2,3), (4,8)) The domain of f =…

Q: 4. Let V1 = (-3) - () -- () 5 = V2 10 V3 = " 12 a) For what values of h is v3 in Span {V₁, V₂} ? b)…

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Q: 6) A function y =e-2x is defined numerically for some data range x. It can be entered using: (а) у -…

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Q: Which of the following sets is a function? * {(a, a)b,b)\a,c)} {(a,b){b,cXc,a} Option 2 О Оption 4…

A: We have to identify which of the following set is a function.

Q: Why the 1st row and 1st column of the JACOBIAN MATRX is always Zero ?

A: It is not necessary that the 1st row and the 1st column is  always zero. It may be possible or it…

Q: Which relation is not a function {(1,5), (2, 6), (3, 6), (4,7)} b. (4,7), (2, 1), (-3,6), (3,4)} a.

A: We have to solve

Q: If Z- tan () then Show that

A: According to question, z = tan-1yx

Q: Which is the graph of the function Ax) - 4/x-2-3? a. C. 10 -10 -8 -6 4 -2 2 4 6 8 10 -10 -8 6 4 2 46…

A: Given: We will graph the above function. Domain of  4x-2-3 :  Solution:  x≥ 2  Interval Notation:…

Q: 10. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. a) f(a) =…

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Q: If the right ray topo log y is considered for the real numbers then [1,5] is closed set O [4, c0) is…

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Q: Consider each of the following relations (x, y) ER, where x = {1, 2, 3, 4, 5} and y E N. Which of…

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Q: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

A: For a,

Q: COSZ 2) if Res(f,x) of the function f(2)=- a) -3/8 b) #-6 2ti c) 1/e d) 8/5 -is

A: To find Resf, π of the function fz=cos zz2 z-π3.

Q: Given F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F(A,B,C,D) and F '(A,B,C,D) in…

A: Solution: Given that F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD Now, truth table Row no.…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Which of the following is the graph of * 4x2 + 13y2 52 %3D 12 V 10 4W2 W2 VF -1412-10 -8-6 -4 -2 olc…

A:

Q: Q1/ Let f, = (! ? 3 45 145 3 ). = (2 6 5).f = (1 345 6 2) € p. Find the following: 1) f, of, 2) 5 3)…

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Q: Compute the Jacobian G(u, v) = (6ue", 3+3e"). (Use symbolic notation and fractions where needed.)…

A:

Q: 34) Deter mine the function at which points, xス f(x ) = if xE if XE IRI& -x2 is contiìNUOUS.

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Q: 12) The value of f, g,f,and g! are given in the table below live f (x) 3. -3 3 6 -2 -1 2. A) Eind h…

A:

Q: Question # 01. Consder z= {acbos a-b =0; S2 Interpet that eguivale nce relation. ~ 18 is

A: That's easy, just show that this relation is reflexive, symmetric and transitive.

Q: Which relation is represented by the arrow diagram? -2 -1 1 О {-2, 0), (-1, 0), (0, 6), (2, 2), (3,…

A: Proceed as shown

Q: How is the Jacobian formulated?

A:

Q: 14. Two variables x and y are given as y = a + bx where a and 6 are constaif show that | r| 1. Or If…

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Q: Question 6 Indicate whether each of the given lines is horizontal (contained in a horizontal plane),…

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Q: 4. (a) Are the points u = independent? (1, 2, 3), v = (-1,0, 1) and w = (5, 4, 3) linearly (b) If…

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Q: Create a vector a with elements = (-1)" 2n (2n)! 1≤n≤ 100

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Q: Compute the Jacobian G(u, v) = (9ue", 2 + 3e“). (Use symbolic notation and fractions where needed.)…

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Q: -2 Let m be a real number and M = {(" ,). )}: 9- If M is a linearly dependent set of M2,2 then m=1…

A:

Q: 5. Prove that for any vector x, we have (a) 1, <H<#H, (b)

A:

Q: 8. If the graph of h(x) goes thro following statements are true fc

A: 8) y=h(x)g =h(x)This transformation only affects y-value.A(-16, 4)y(x=-16)=4, g(x=-16)=4 =2A' (-16,…