Give an example of a linear operator TE L(R*") which is not diagonalizable. Justify your answer.

Q: u+ 4 dy 5. If y = and u = Vx + x find when x = 4. dx u- 1

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Q: How many shortest lattice paths start at (2, 2) and a. end at (10, 10)? b. end at (10, 10) and pass ...

A: Note: As per our guidelines, we are supposed to answer only 3subparts and rest can be reposted.   Fo...

Q: (Q4) Prove that if f : R → R is continuous function, and (n¡)ieN is a sequence of non-zero natural n...

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Q: Show that if E1 and E2 are measurable, then m(E U E2) + m(E1n E2) = m(E1) + m(E2).

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Q: x1 + x2 + x3 = 2 20x1 + 2x2 - x3 = 25 2x1 + 13x2 - 2x3 = 30 Linear algebraic equation set x1 (0) ...

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Q: Let y be a solution of the differential equation 2 * - (). T+y- I+y+I where x + y +1>0 for all x,y s...

A: Differential equations

Q: What is the result of combining aifferent shapes whetner repeated or altered to create a cohesive de...

A: Given: Different shapes. To find: What is the result of combining different shapes whether repeated ...

Q: a² sin(2y – 52) =1+ycos(6zx) 4.xsin(2y – 5z)+ sin(2zx)6zy O A. cos(2y – 52)(-5)a² + sin(3zy)6xz 4.xs...

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Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrang...

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Q: Find the perimeter of the loop of the curve 9y? = x² (2x + 3). O 2/3 units O 3/2 units O V3 units No...

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Q: Let h, k, r, m, t E R. A general equation that corresponds to the above surface is: (x – h)² _ (z – ...

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Q: Let 4 VA v3 %3D vi -2 9. where cER. What is the only value of c for which the set {v1, v2, V3, V4} i...

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Q: Prove using the formal definition of a limit that the following sequence converges: +00 S-n3 + 2n – ...

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Q: Using ɛ-d argument, prove that f(x) = x-[x] is continuous at all x ERexcept the integers. (Note: [x]...

A: Solution:-

Q: The amount of pollutant M in the atmosphere is decreasing with time t according to the formula M = e...

A: For a function: y=f(x), the dependent variable is y and the independent variable is x. The value of ...

Q: Let P (A) = 0.4 and P (A ∪ B) = 0.6. For what value of P (B) are A and B independent?

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Q: differential equations. dy 1. - 16y = 0 - dt2 dy 6- dt 2. + 8y = 0 dt2 d'y dt2 3. + 1?y = 0

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Q: Find k such that the function is a probability density function over the given interval. Then write ...

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Q: In a batch of 500 high school students, there are 252 students who own a laptop, 176 students who ow...

A: Here we can use the formula nU = nA+nB-nA∩B+nA∪B' 

Q: Use Newton-Raphson method to solve the following simultaneous nonlinear equations assuming x(0) = -0...

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Q: Salue-

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Q: test the following series. whether absolute convergence, conditionally convergent, or divergent! a) ...

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Q: ()- For and a point P e R°, we have = -1. . Determine the value of (").

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Q: N A, = U A 1<i<n 1<i<n

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Q: (8) The trace and determinant of positive semidefinite matrices are numbers. nonnegative real

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Q: Evaluate the below exprassion

A: Given,          1+i10

Q: ing False-Position Method, find the Root of the following equation: - 3. x = 0 for the interval (0.5...

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Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that sa...

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Q: Determine Whether the Series is convergent ordivergn. Write the exact test that you US e, 2n-1 Sin T...

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Q: 20. Prove that an angle of 0 radians is constructible if and only if the real number cose(sine) cons...

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, xz ...

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Q: Find the unknown values for triangles with given parts. a = 385.4, b = 467.7, c = 800.9 a C O A = 18...

A: Solution:-

Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (2, 4, 6), (6, 3, 2)}...

A: Since S contains zero vector, it is not linearly independent.  a(0, 0, 0) + 0(2, 4, 6) + 0(6, 3, 2) ...

Q: Consider a, B = 0. A possible graphical representation for the equation plane ax = By is: A) B)

A: Given  α,β≠0.we have to find the graphical representation for the equation plane.αx=βy

Q: Suppose the initial mass of a radioactive isotope was 80 g and the half-life of the material is T. T...

A: The half life corresponds to 12 of the given material  Therefore after three half lives 12×12×12 the...

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0 ...

Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the polynomi...

A: Solution:-

Q: Let y be a solution of the differential equation y = 3, where x > 0, y > 0 2ry such that y(2) = 6 . ...

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Q: Question 1 Determinants (a) Find the determinant of the matrix [1 r A = where z e R. (Hint: Use row ...

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Q: The volume of a section in a thread is given by=V = 4Sinx(1 + Cosx). What is the value of x that giv...

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Q: Hw.4 consider a ctosed Kectangutar box uith a If base side ir measured with evror at 2% and the heig...

A: Volume of the box with square base is given by V=x2ywherex=base sidey=height Surface area of the box...

Q: 3. Find the transformation fourier function from the following exponential function: fk) = e " jika ...

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Q: ind and classify all critical points of the function f(x,y) = 3x²y + y³ – 3x² – 3y² + 2.

A: We have to find and classify the critical point of f(x,y).

Q: Let y be a solution of the differential equation * + (1+ )y = !, where x > 0 such that y(1) = 1+2. I...

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Q: if |f] is in L^1(A), then his in L^1(A)?

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Q: Let Gbe an open set in R". Two points x, Y e G are said to be equivalent if they can be joined by a ...

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball...

Q: Being fa differentiable function. Consider the relation where z is implicitly defined in terms of x ...

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Q: A model for the velocity v of a skydiver is 4 = 9 – v². Then the value lim v(t) is Enter the correct...

A: First Order differential equation  

Q: #1. Use mathematical induction I to prove that for all integers n 2 3, 2·3 + 3 · 4 +. + (n – 1) · n ...

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Q: 2. Consider a square ABCD and an equilateral triangle BCE in its exterior. Let F be the midpoint of ...

A: Given figure is Since ABCD is a square and ∆BCE is equilateral . So DC=CE