D) How do you know that T: P3> P2? (How do you know that the codomain is correct?) E) Find T(x + 2x? + x + 4) F) Find, if possible, a basis for ker(T), and state the nullity of T.

Q: Am.111.

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Q: The set B = {3+4x², 12 − 3x + 16x², 9x - 25 - 36x²} is a basis for P₂. Find the coordinates of p(x)…

A: Here we have to find the coordinates of p(x) relative to the basis B.

Q: The set B=(3+2x², 12+2x+8x²,- (29+6x+20x2)) is a basis for P2. Find the coordinates of p(x) = 8 + 4x…

A: Solution :-

Q: 4 1 7 - - - - H -3 V2 = 9 14 11 , and also let H = Span{v1, 02, 03}. 7 -2 6 It can be verified that…

A: It can be verified that Using this information we have to find a basis for H.

Q: [4 3 8] Q6. Write the basis and dimension of the row space and column space of A = 3 2 l2 2 2) 1.…

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Q: The set B = {4 — 4x², 12 - x - 12x², 33- 3x - 32x² } is a basis for P₂. Find the coordinates of p(x)…

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Q: {(:}) (::). (; })· (; )} 1 1 1 2 2 3 3 4 2 2 3 4 5 1 7 3

A:

Q: Answer all the questions: (2 1 1 1. The characteristic polynomial of the matrix 0 1 0) is A1 1 2. a)…

A: Here the given matrix is                                        211010112 We have to find the…

Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: Use the fact that matrices A and B are row-equivalent. 2 10 0 5 1 1 0 3 7 22-2 15 34 11 2 4 10 30-4…

A:

Q: :) The set B = {-(1 + x²), 3x − 4 − 4x², 7 - 6x + 6x²} is a basis for P₂. Find the coordinates of…

A: Let us consider the element v and B be the basis then,  To write the vector v in the linear…

Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the…

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Q: (4) 10. Let H = {r+2x2, 1+ ka?, k + (2k + 3)r2} (a) For what value(s) of k is H linearly dependent?…

A: This belong to linear algebra.we check linear independence for the given vectors and find k so that…

Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

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Q: Explain why S is not a basis for P2. S = {1, 6x, –9 + x², 7x} O Sis linearly dependent. O S does not…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 3x + 4x²} O s is linearly dependent. O…

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Q: The set B = {− (1+3x²), − (2+2x+6x²), − (6+4x+21x²)} is a basis for P2. Find the coordinates of p(x)…

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Q: Let B = {1,1+x,1+ x + x² }. (a) Check whether that the set B is a basis for P2. 2 (b) Let p(x) =…

A:

Q: asis: The set B = {2-3x², 8+x-12x², 33x² - (21+ 2x)} is a basis for P₂. Find the coordinates of p(x)…

A:

Q: etermine whether the set S = {1-3xr?, 2x+5x²,1-x+3x²} is basis for P,(R).

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} O S is linearly dependent. O…

A: Consider the given functions. S=1-x,1-x2,-1-4x+5x2 Let S is linearly independent and there exist…

Q: Extend {1 + x, 1 + x + x2} to a basis for P3.

A: Given set is ,                  1+x , 1+x+x2   (.)  Standard basis of  P3  is                    1 ,…

Q: - Suppose that f(x) = x² + 1, g(x) = x² - x and h(x) = x − 1. Then the set of functions {f, g, h} is…

A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:

Q: Use the standard basis for P2, B = {1, t, t²}, and the coordinate mapping to show that 10 – 12t –…

A: The solution is below.

Q: 20r1 – 10r2 5r1 + x2 < 8010 -2r1 + 3r2 < 700 I1, 12 2 0 max subject to: . Consider the following LP…

A: We will answer the first questions since we answer only one question at a time. Please resubmit the…

Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x², 8x} S is linearly dependent. O s does not…

A:

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.