Let V={a0+a1 x+a2 x2 | a0, a1, a2∈R} be a vector space of polynomial up to degree three, and p(x)=p0+p1 x+p2 x2, q(x)=q0+q1 x+q2 x2∈V then =p0.q0+2 p1.q1−p2.q2 is an inner product True or False

Q: Identify the maximum value and the corresponding unite vector of the quadratic form Q = x1 3a²³ —…

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Q: At a certain University every student ID number starts with a 2 and each ID has 8 digits. Suppose…

A: The students are the pigeons, the possible sums are the pigeonholes. We map each student to the sum…

Q: In order for vectors and t- 3 in a vector space R3 to be linearly t+4 in depen den t what should t…

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Q: - c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Fine the vector y by the…

A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: (a) Let A (b) Let A = = x = 1 1 arbitrary mx n matrix and x = = What are the row vectors and column…

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Q: 3- The vectors x, = R3, are linearly independent. (1,0,1), x2 = (-1,0,1) and x3 = (-2,4, –3) in O…

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Q: 1 2 0 0 3 1 -1 2. Express 14 as a linear combination of the columns of A = Then 2 0 0 1 find a…

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Q: Either use an appropriate theorem to show that the given set, W, is a vector space, or find a…

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Q: Find a least-squares best fit line for the points (1, 5), (2, 1), (3, 1), (4, 3). Write your answer…

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Q: 4. Determine whether or not the following functions are linearly independent in the vector space P4.…

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Q: show that the given vector functions are linearly dependent on (−∞,∞).

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Q: The following table gives the data collected in an experiment to study the relationship between the…

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Q: 4. Prove that, for any vectors A, B and C, a necessary and sufficient condition that A x (B x C) =…

A: Given: Three vectors A,B, and C. To Prove: necessary and sufficient condition for A×B×C=A×B×C, is…

Q: Consider the vectors U₁ = 2x² + 2x - 1 and U₂ = -x² - 3x + 1 in P₂. Which of the following vectors…

A: Vectors v1=2x2+x-1 and v2=-x2-3x+1. To find the vectors that are linear combination of v1 and v2.

Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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Q: Is the set S linearly independent? Yes No

A: We have to find

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: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: Determine whether or not W = {[a, a?, b] | a and b are real numbers} is a subspace of R³. Justify…

A: See the detailed solution below.

Q: Sketch all four subspaces associated to mat 1 2 A = 3 6

A: Respected student, By Bartleby guidelines we have solved all the four subspaces with the first…

Q: Select one: a. S={ X2 %3D b. , X €R} S={ 1 C. X 1 X1=2x2} X2 O d. S={ X1=X2}

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Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: Find a basis of the subspace of R³ defined by the equation 2x1 + 3x2 + x3 = 0.

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Q: Solve the initial value problem. 5 -2 2. X' = AX, X(0) = where A = 10 -2 O A. X(t): [-2 sin 5t + 4…

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Q: Given the set R² with the vector addition operation defined by (x₁₂1₁) (x₂, 1/₂) = (x₂+x₂₂3₁ +3₂ −2)…

A: Given a vector addition operation, we want to find the zero vector for the set .

Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Q2. Show that M2x2 , the set of all 2× 2 matrices is a vector space. Explain your answer? Good Luck!

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Q: Show that every subspace of ℝ is either {0} or ℝ.

A: Given: ℝ. To Show: Every subspace of ℝ is either {0} or ℝ.

Q: Determine if set S is a subspace or not S = {(a,0₁0) € R² } Ⓒ @ 3 S = {(₁₁ 6₂c) | b=a+c} in R (3) S…

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Q: If a, and b are non - collinear vector and vectors a = (x +4 y)a +(2x + y +1)b and, B= (-2x + y + 2…

A: We will solve the following

Q: Let W be the subspace of Rª defines as X1 X2 W = {x = ER : : x1 – 3x2 + 4x3 – x4}. %3D x3 X4…

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Q: Q1. Which equation can show the "linearity" of Ordinary Least Square (OLS) assumption? A) Y=B1 +…

A: A linear regression equation only sums the terms in the model while the model must be linear in the…

Q: Determine whether W = {ao + a1x + a2x² + a3x°|ao + a2 = az ɑ1} is a subspace of P3.

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Q: the dimension of the complexification VC thought of as a real vector space

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Q: The rectangular box shown has sides, EH of length 2, EF of length 4, and HD of length 5. A(0,0,0) is…

A: Your question is : find the distance between BB and line GM. I think you want to ask distance…

Q: 1 (a) Is the vector 2 in the span of -1 and 2 ? Justify your answer 3 1 (b) Is the set linearly…

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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.