Let B = {1+t,1 – t} and C = {4, 1 + 5t, t²}. Does B form a basis for P2?

Q: The set B = {2 - 2x², 6 - 2x − 6x², 13 - 6x - 12x²} is a basis for P₂. coordinates of p(x) = 18x −…

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Q: The set B = {4 – 2x2, 20 – 2x – 10x?, 54 – 4x – 26x²} is a basis for P2. Find the coordinates of…

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Q: The set B = {4x²3, 12x² (9+x), 38+ 3x - 48x²} is a basis for P₂. Find the coordinates of p(x) = 44+…

A: Given; B=(4x2-3, 12x2-(9+x), 38+3x-48x2) p(x)=44+3x-56x2

Q: Which of the following is a basis for R2? (a) {(1,-1),(-1,1)}  (b) {(1,−1),(1,1),(−1,1)}  (c)…

A: Let V=ℝ2. Identify the basis of ℝ2.

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t +t, and let…

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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: Given 4 1 -3 -1 2 A = 3 4 -6 8 0 -1 3 Find a basis of the row space of A.

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Q: Find the coordinate vector [p(x)]B of p(x) = x² + 4x + 4 with respect to the basis B = {x³ + x – 2,…

A: According to the given information, it is required to find the coordinate vector.

Q: The set 1 -2 ГО [o oj В - -3 0 2 is a basis of the space of upper-triangular 2 × 2 matrices. -6 -6]…

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Q: Which of the following is a basis for R? O a. {(1,0), (2,0)} O b. (1,2), (2,3), (1,7)} O c.…

A: We have to check

Q: Determine whether S is a basis for P3.S = {4t − t2, 5 + t3, 5 + 3t, −3t2 + 2t3}

A: The given set is S=4t-t2, 5+t3, 5+3t, -3t2+2t3. Check whether the set S is a basis for the vector…

Q: Determine whether the set {x2 + 2x - 3, 2x2 + x - 1, 3x2 + 2x - 2} is a basis for P, by solving the…

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Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

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

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Q: Define R4 R³ as follows T-5 0 -2 01 Tx= 5 -4 2 2 x 10 -4 4 2 Write your answers as a matrix whose…

A: Teh given transformation, defined as..The aim is to find the basis for the image and kernel of .

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: Find a basis for the null space of the matrix. [10-7-2] A = 01 7-2 00 0 0

A: The given matrix is A=10-7-2017-20000. We have to find the basis for the null space of the matrix.

Q: Find the change of basis matrix [B]. {0}{000) C = B = -2 -3 2 -2 -31 2 4 5 -3

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Q: Explain why S is not a basis for P,. .2 S = (1 - x, 1 - x², -1 – 8x + 9x²} O s is linearly…

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Q: Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to…

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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: 2 10 6 - Given A = 4 20 12 a. Find the basis for the row space and column space of A. b. Find the…

A: The given matrix: a) To find the basis for the row space and column space of A:  Apply some…

Q: c. If a matrix has more columns than rows, then the dimension of the column space is bigger than the…

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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: The set B = {2 + 3x², 10 + 4x + 15x², 26 + 8x +36x²} is a basis for P3. Find the coordinates of p(x)…

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Q: The set B = {2+ 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x) =…

A: Given Basis: B=2+2x2, 4-3x+4x2, 19-9x+18x2. To find: Find the coordinate of px=84-39x+80x2 relative…

Q: -3x + 6y - z +t - 7v = 0 x - 2y + 2z + 3t - v = 0 2x - 4y +5z + 8t - 4v =0 Find the solution space…

A: Dimension = number of linearly independent vectors in basis.

Q: Given the ordered basis 5 3 -9 B = { A1 A2 -1 8 4 -1 ,A4 -7 Аз -3 -4 -5 32 -28 find [A]B, the…

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Q: Find a basis for the rowspace, columnspace, and nullspace of the following matrices. i 4- i (b) B =…

A: We need to find the basis for the row space of matrix A.  Now, matrix A is: A=222i2i2i21+i1+i-1-i…

Q: 26. In P2, let Q = {pi(x), P2(x), p3(x)}, where P₁(x) = 1 + x + 2x², p₂(x) = x + 3x², and P3(x) =…

A: From given basis B of P2 let us prove Q also forms the basis of P2.

Q: 1 2 1 01 2 5 1 1 Given A = 3 7 2 L4 9 3 -1 Which of the following is not a basis for row space of A?…

A: We have the matrix A=121025113722493-1 First, we find the row reduced echelon form of the matrix 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.