Determine whether S is a basis for P3.S = {1 − 2t2 + t3, −4 + t2, 2t + t3, 5t}

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A: The sequence is 1,3,11,31,69The sequence of first differences is(an+1 - an) = 2,8,20,38The sequence…

Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions

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Q: 7. 1 -2 3 1 30 -5 7 52 1 2 - 2 4 1 -3

A: Given: Objective: To find the determinant by row reduction to echelon form.

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A: The solution is given by

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Q: 2. Prove: a. [(x)b~ XE]~ = (x)b XA b. Эх (~p(x) A ~q(x)) = ~[Vx(p(x) V q(x))] 3 Dariva

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Q: find the associated partial differential equation to solve Z= f(x + ay) + g(x+by)

A: To Find:Partial differential equation using the above equation.

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A: We can express the distance between the tower and each city using the distance formula: distance =…

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A: Fundamental solutions of the given DE is 1, t, t2, e2t, sin(4t), cos(4t), tsin(4t), tcos(4t).

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Q: Problem 4 Let A, B, and C be sets. Use the facts that the Symmetric Difference is associative and…

A: are sets.

Q: Part II: Match each function with its graph. Give reasons for your choices. 1. f (x, y) = 1 x+1 +…

A: We have to match the following graph

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Q: II) 3100 - = a) ak-1 ... 01.00) = a0 =? 7 7D

A: Exponent series expression :

Q: M (x₁+x2) dV2(x), where M is the 2-manifold in R4 given parametrically as shown. x = (U₁+U₂,4₁…

A: The solution is given by

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Q: Consider the following initial value problem: 0≤t≤7 t>7 y" + 25y = (7, 10, y(0) = 7, y'(0) = 0 Using…

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Q: 13. r' = x² + x + 1

A: To find the equillibrium points, we need to find the root of x'=0.See the solution below.

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Q: (y-5) (3,7) 5 units away say find all the valub of y. distance formula use D= √(x²₂³x)² + (Y₂= y)²

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Q: What about the part where it has to be part of the curve r= sqrt(2cos(2theta))?

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A: A function To Find:Value of  for which the function is the inverse of itself.

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Q: 2² L 7s+2 7s+2 C-²{(5²+ - 2)2} +2)(s-1)(s-2)] S²+2)(S-1)(5-2) 2 1 As + B (5²+2) + 23/25 - 11/12…

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A: Given: Objective: To find the value of  in the logarithmic form , where , using the equation .

Q: A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space,…

A: A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space,…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.