Let u1 = (1, 3, 2, 1), u2= (2, −2, −5, 4), u3 = (2, −1, 3, 6). If v = (2, 5, −4, 0), write v as a linear combination of u1, u2, u3. If it is not possible say so

Q: 1. Consider the set V of all polynomials of degree two or less, along with the following definitions…

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Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: If B has a column of zeros, then so does BA if this product is defined. True O False 4

A: Given B has a column of zeros , then to find BA has a column of zero or not .

Q: Let S = {1+ 5x, 1 – 2x-}. Which of the following polynomials could be added to the set S to form a…

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Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

A: Use the results and roperties of diagonalization of matrix to solve this problem.

Q: Exercise 9.2.6 For each of the following sets of polynomials, determine whether the set is linearly…

A: The set  is linearly indepemndent if Otherwise linearly dependent.

Q: a= b= C= id=

A: As per the question we are given a two dimensional set V and we have to find the values of a, b, c,…

Q: Show that the set of all second order polynomials, f(x) = ax² + bx+c, is a vector space.

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Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

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Q: Show that A= 4 * eye (4) - ones (4, 4) is not invertible: Multiply A* ones (4, 1).

A: We have to show that:  A= 4 * eye (4) - ones (4, 4) is not invertible

Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Determine whether the following set of polynomials is linearly independent (1 – t)?, t – 2t2 + t³,…

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Q: The Hamacher product is the t-norm given by ab t(a,b) = a +b – ab Show that this function satisfies…

A: Here the Hamacher product is the t-norm given by t(a,b)=aba+b-ab We have to show that this function…

Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

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Q: A Show that the function f: R² → R defined by f(x₁, x₂) = x² + 2x² + 3x₁x₂ + 4x₁ + 5x₂ + 6 is a…

A: Definition of Vector Quadratic Function : Given Function f: R2→R is a vector quadratic function if…

Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

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Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

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Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

A: We have to describe the zero vector (the additive identity ) of the vector space P3.

Q: The set of polynomials {3t²-3t+5, mt+6t²+10} is a linearly dependent set in P, if 2 m=6 Select one:…

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Q: Let P₂ (R) be the vector space of polynomials of degree at most 2. Which of the following are…

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Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: 2. (a) Define the dot product of two polynomials p(x) = ao+a₁x+a₂x²+a3x³ and q(x) = bo+b₁x+b₂x²+b3x³…

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Q: d) the transpose of x. 2- If x= [2 8 5; 9 7 1], b=[2 4 5] find: a) find the maximum and minimum of…

A: Given:x=285971 and b=245To find:a) The maximum and minimum of x.b) add the vector b as a third row…

Q: Prove that in P2 (the set of all polynomials with degree n< 2), every set with more than three…

A: Linearly dependent set:  A set of vectors α1, α2,α3, … ,αn is said to be linearly dependent if ∃ c1,…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.