Problem 5 Short answers: (No explanations needed. Simply write your answers. If you do some calculation to get the answer, show the calculation.) (a) If 4 is an eigenvalue of a matrix A, then what is det (A-41)? (b) Suppose T: R¹ R³ is an onto linear transformation. What is the dimension of range of T?

Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

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Q: Give all the integer solutions of the congruence 56x-12=0 (mod 23).

A: Given congruence 56x-12 ≡ 0 (mod 23) i.e., 56x ≡ 12 (mod 23) i.e., 10x ≡ 12 (mod 23) We know that,…

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Q: 4. Find the derivative of f(x) - 7. A. 7 B. 0 5. What is the derivative of In(x)? A. xln(x) B. 1/x…

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Q: 11: Given the function f(x) = 8x² - 4x₁x₂ + 5x² and Xo = [5 2]. Then G-¹g at Xo is equal ((G is the…

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A: Introduction: A permutation is the arrangement of objects. When a certain number of objects are…

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Q: In each of Problem, find a fundamental matrix for the system with the given coefficient matrix. (1 5…

A: Consider the given coefficient matrix, A=150010481 here we need to find a fundamental matrix for the…

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Q: * Consider the following matrices /1 1 1/2 3 4) ^ - (-: 2) - - († ;) -- ( 7² :¦ ¦) -- () --(:::;) A…

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Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

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A: Matrix B is found by comparing entries

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Q: 3 co ós co -6 -3 144 -4 Let y = ,V1= 5 -1 Compute the distance d from y to the subspace of R4…

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Q: 1. Find the Fourier series of the function f(x) = |x| which is defined over the range - T<x< T.

A: f(x) is periodic with period 2π  f(x) is continuous except at the end poits (where f is not defined)…

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Q: 3: The cubic interpolation method with two points has converge rate with order three. True False

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Q: Evaluate the z transform of x(n)= a(n) u(n)

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Q: 4. Given the data below: x 1.0 1.2 1.4 1.6 1.8 2.0 f(x) 2.2183 2.6001 3.0752 3.6730 4.4296 5.3891 i.…

A: The 3-point backward formula f'(x0)≈f(x0-2h)-4f(x0-h)+3fx02h

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Q: 3) You deposit P 12,780.00 in an account paying 93% simple interest. Find the future value of the…

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Q: 2. Using an appropriate method, compute the following integrals. x² dx x² + 3x +2° (i) sin³x cos*x…

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Q: Hand written piz In each of Problem, find a fundamental matrix for the system with the given…

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Q: companies that sell identical products. Compan or Php 27. Meanwhile, Company 2 can sell the e…

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Q: 7.1.1. Find the Fourier transform of the following functions: (a) e−(x+4)², (b) e¯\x+¹, x, |x|<1,…

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Q: 3 -6 -4 -3 4 Let y = V₁ = 1 1 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁…

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Q: 3 -1 -6 -4 -3 4 Let y = D-B V1 = 5 -1 Compute the distance d from y to the subspace of R4 spanned by…

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Q: For which real numbers k is the matrix [3] k -31 A: k> 3 B: k=3 C: k <3 3 positive definite matrix?…

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Q: H.w 3: Apply the Trapezoidal rule to evaluate Sofia+ 2xydxdy (1+x²)(1+y²)' 2030 10+ PILO)S…

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Q: x=3 Qs. A: Find * x²dx by using Riemann integral.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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A: Law of sines for the triangle △ABC. sin Aa=sin Bb=sin Cc

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A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Construct a triangle ABC having AB= 75 mm, angle ABC = 45°, and angle BAC = 60°. Without measuring…

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Q: 1 2 If R = 3 1 that R² = 2R + cS. and S= 1 1 0 0 1 find a number c such

A: Solving matrices question by finding square of R matrix

Q: 7. By separating a) b) the variables convert the PDE into a system of ODES Sem азт а т + д?хду дхду…

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Q: Question: iz -iz (a) Let f(z) = e + e 2 Go show that f is periodic with real period 2Ã

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

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Q: Se²x s sin 2x dx 1. Solve (i) The integration by parts method. (ii) The tabular method. using the…

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Q: 8: [1 The matrix A = 4 L3 O True O False -2 31 1 -1 - 2 is a positive definite matrix. 21

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Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3