Show that the set of all matrices of order 2×2 of the  form \matrix{a|0|b|c}, where a,b,c are integers is a subring of  the ring M of all matrices of order 2×2 with integral  elements.

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Q: Consider the vectors u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = =…

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Q: The linear sum of two subspaces of a vector space is also a subspace.

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Q: S da 49+25x² f(x) ve f(3) = 0 ise f(0) = =?

A: The given integral is .Also given that .

Q: 43. Find the first partial derivatives f(x, t) = e-t sin(x) g(x, y) X (x + y)² h(x, y) = tan ¹(y/x)

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Q: Given F = (2-2yz)i + (y+xz)j + (xy + z2)k and S the surface z² = x² + y² where 0 ≤ % ≤ 4. Use…

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Q: Suppose that f(x, y) = x² − xy + y² − z +y with D = {(x, y) |0 ≤ y ≤x≤ 1}. 1. The critical point of…

A: Suppose that f(x, y) = x² - xy + y² -x+y with D = {(xy): 0 ≤ y ≤x≤ 1}.1. The critical point of f(x,…

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Q: Let G be a group of order pq, where p and q are distinct primes and p > q. Then (i) G has a normalo…

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Q: Find the Laplace transform F(s)=L{f(t)}} of the function f(t)=(5−t)(h(t−3)−h(t−7))), for s≠0…

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Q: Let r(t) = (t², 4t-3). (a) Find T(t) and N(t). (b) Find the decomposition of a(t) into its…

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Q: Consider the following initial value problem: y′′−4y′−45y=sin(5t)     y(0)=7,y′(0)=5   Using Y for…

A: The given initial value problem,.We have to find the Laplace function using the Laplace transform.

Q: Let A = 21. (a) Compute A², A³, and A4. 02 (b) Find a formula for A" for any integer n ≥ 1?

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Q: Consider the function. f(x, y) = 2(y + 1)x² Identify the point(s) on the graph of f at which the…

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Q: Transform the differential equation 2y′′−y′+4y=e^(mt) y(0) = 2  y'(0)= 5 a )into an algebraic…

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Q: [] Let y = [8] and u= Compute the distance from y to the line through u and the origin. The distance…

A: Given:  and To Compute: The distance from  to the line through  and the origin.Formula for…

Q: Describe 72 minus 56 using the abstract approach of CSA

A: We have to describe 72 minus 56 using the abstract approach of CSA.

Q: To find the Laplace transform of e^(6t)cos(at)you would substitute  into s/(a2+s2) which gives ?…

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Q: C 2 A 17 F 2 D 14 13 7 E 10 B 16 8 4 G 1 ☺ K L 6 15 5 11 H 18 9

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Q: A collection of 226 coins consisting of pennies, dimes, and quarters has a value of $16.60. Five…

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Q: Write a function (in any form ) with each characteristic A quadratic function only 1 root: x=9 A…

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A: Given two variable function is                     f(x, y) = 5 − 2x + 4y − x2 − 4y2We have to find…

Q: Choose the correct one for the constrained maxima and minima for f (x, y) = xy given that x² + 3y² =…

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Q: Q2: Consider the following table: x 0.800 1.000 1.200 1.400 f(x) 1.040 1.151 1.213 1.228 a. Estimate…

A: note :Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Speedometer readings for a vehicle (in motion) at 4-second intervals are given in the table. t (sec)…

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Q: Select the option that contains the inverse of the following Laplace transform F(s) = = 1-e-T8…

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Q: i want mathlab code for steepest ascent method to solve this problem 4x+2y+x2-2x4+2xy-3y2

A: Equation :

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Q: Calculate the amount of money you'll have at the end of the indicated time period, assuming that you…

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Q: (x² - 1)y" + 4xy + 2y = 0, y(0) = 1, y'(0) = -1 ∞ This problem has a series solution of the form y =…

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Q: Let f(u, v) = (u - v, 1, u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first…

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Q: Let R be the field of real numbers, show that the set W={(x,2y,3z):x,y,z∈R} is a subspace of a…

A: The given set .We have to show that is a subspace of .

Q: In the following decomposition, we needed two fractions because the linear factor is repeated twice.…

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Q: 6. Let 1-2 A ^= (²-²² ₂²³). G (a) Find bases for N(A) and R(AT). (b) For an arbitrary z € R³, find…

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