Let v1, v2, V3 R° and suppose {v1, v2, V3 } is a linearly dependent set. Let A = [v1 v2 v3] E R5×3. Prove there exist infinitely many solutions 7 E R3 to the equation A = ö.

Q: For which value(s) of s, if any, v1, Let Vi V3 S 1 V2 and v3 are linearly independent.

A: For linearly independent, mode of matrix of vector is zero.

Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

Q: Q5: a. Find * and for u - p=x+y+z ,and q = x+ y+ z, and r=x+y-z, at the point (x,y, 2) = (v3, 2,1).…

A: a)                          u=p-qq-r                             p= x+y+z;…

Q: If an object is moving with v(t) = 3¹ and the position X(1) = 2, what is the position of the object…

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Q: Evaluate f a'y*da + =*ydy counterclockwise around the square with vertices (0,0), (1,0), (1,1), and…

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Q: If C is the z-axis from the origin to the point (0,0, 2), then So(3j – 3k) - d - dr |

A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

Q: Find the following statement is true? ' W[y1,y2] = 0 implies y1 and y2 are linearly dependent'

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Q: If |r(t)| = c (a constant), then r' (t) is orthogonal to r(t) for all t.

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Q: Let A = {a1, a2, a3} and D = {d1,d2, d3} be bases for V, and let P = [ [d¡]a [d2]A_ [dz]a ]. Which…

A: We will use the following theorem to find the correct option.  "Let B=b1, b2, b3,...,bn and C=c1,…

Q: 1. Let u = 2î + j- 2k, v = 12î – 4f + 3k and w = 4f + x?k c. Find x such that u and w are…

A: u = 2î + j- 2k, v = 12î – 4f + 3k and w = 4f + x?k

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: 2. F = (1+ 2y)i + (r + e")j, and C is the triangle with vertices (0,0), (1, 1), and (-1, 1),…

A: 2) Given vector field F→=x+2yi→+x2+eyj→. To find ∫CF.→dr→ where C is the triangle with vertices…

Q: Suppose b, c E R. Define T: R³ → R² by T(x, y, z) = (2x − 4y + 3z + b, 6x + cxyz). Show that T is…

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Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

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Q: B- Let r(t) = (²+2) i + (3t) j .Find (t) such that r(t) parallel to r'(t).

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Q: Hw.L showthat Vi=3inbj andVz 2-i-zj have opfosite directions.

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Q: Find a relating ab and c Sothat the linear Systen X +2y- 2X +3 y +3Z = 6 5X +9y - 6Z = c eojarrar A…

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Q: Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

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Q: Let T : M2(R) → P3(R) be defined by       ( a b) T   (c d ) = dx3 + ax2− bx − c. Determine whether T…

A: Here, the given transformation is: T:M2(R)→P3(R) where Tabcd=dx3+ax2-bx-c

Q: 6. Let V₁, V2, V3 R³ be nonzero such that v3 E (v₁, v2), but v2 # (v₁). Which of the following is…

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Q: If g = xy + yz + zx and Ē = x²yī+ y²zī+ z²x k, find F. grad g and cross product of F and grad g at…

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Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

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Q: Find all values of h such that {t² + 2,5t² + t - 7,-4t² - t + h} is a linearly dependent set in…

A: We are given a set of 3 polynomials in polynomial space P2[t] , including a unknown parameter h And…

Q: The functions y, = e* – e-X a y2 = - 3ex + 2e-x are linearly independent. True False

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Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

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Q: Which of the following are first order linear aiterential equations? F. = y – 3y

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Q: (d) Let A E M3x3(R) and , ij, Z ɛ R* and they are linearly independent. Suppose that we have A = ,…

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Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

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Q: Consider the linear operator T: R? → R² defined by the following equations. w1 = 3x1 + 11x, W2 = X1…

A: we have to find the inverse of T          (i.eT-1(w1,w2))where T:R2→R2 is given by…

Q: Show that u = (a, b) and v = (e, d) in K? are linearly dependent if and only if ad – be = 0.

A: Solved below

Q: 2. Determine if each of the statements below is true or false. If a statement is true then prove it.…

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Q: All points x, y) in the plane equidistant from (1,7) and (-1,5) satisfy which of the following…

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Q: Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property…

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Q: (b) By determining constants c,, C2, C3 and c4, which are not all zero and are such that cifi(x) +…

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Q: M1 := sup ||T(x)|| and ||x||=1 M2 := inf{C > 0 : ||T(x)|| < C||x|| for all x e R"}. a) Prove that M1…

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Q: (a) Determine if the following sets of functions are linearly dependent or linearly independent on…

A: We are entitled to solve only one question at a time. Please post other questions separately. To…

Q: 1. Show that the functions e*, e2*, e3*are linearly independent. Show Complete Solution Answer: W 2e…

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Q: By determining constants C1, C2, C3, C4, which are not all zero and are such that C1 f1 + C2 f2 + C3…

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Q: Let T : R² → R³ be the linear map given by [2r1 + 7x2] 2i + 22 Write does the matrix A associated…

A: The given linear map is T:ℝ2→ℝ3Tx1,x2=2x1+7x2, x1-x2, x1+x2 To find the matrix A associated with T…

Q: The functions y1, Y2, · . . , Yn are linearly independent, if and only if W (y1, 22, *. Yn) (to) # 0…

A: Consider the following differential equation, y''+pxy'+qxy=0

Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: If two functions yı(t), y2(t) E C^ (R) are linearly independent, then y (t) and y, (t) must also be…

A: Suppose that there exists functions f f and g g defined on the real numbers and differentiable…

Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: 3. Determine whether the functions e and re are linearly independent or dependent by calculating…

A: f= {e^2x , x.e^2x} is Linearly independent if Wronskian is non zero.

Q: Let Ti P(R)→ Pz CR) ope natag T(2+x)=D1 Expilain ke a liness Seech that T (1) = 0. and T(1+x²) = 2x.…

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Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: Q2) The seraight s line (1,0, 1) +e(2,1,1) intersect The plane X+2y-3#=0 at the point (O,O. D)

A: