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

Q: Determine if the rows of S are linearly dependent or independent. 1 1 01 1 3 2 1 3 1 1 S = 1 2 1.

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Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)…

A: In this question we have to find the basis for the nullspace of the matrix.

Q: Suppose f: R² → R² is a linear transformation. The two pictures on top in the figure use standard…

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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: Let B and C be bases for P2. If B= {x, 1 + x, 1 -x + x2} and the change-of-basis matrix from B to C…

A: It is given that,  B and C be the bases for P2  and  B = x, 1+x, 1-x+x2. The change of bases matrix…

Q: -6 -2 -2 0 -6 -2 -2. Find a basis for N (A), the null space of A. Let A = [ 0

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Q: { 1 + x + x², x + x², x²}. %3D for P2. Let p(x) = -1 +x + 2x2. Then [p(x)]B = %3D %3D

A: The given basis is B=1+x+x2,x+x2,x2 for p2. let p(x)=-1+x+2x2 We have to find,  p(x)B=?

Q: Find the change of basis matrix [] and use it to find [v]• B -17] 2 0 --{@@@}-E -2 4 4 B 1 2 = -71…

A: Given Information: and To find: and Notation used: denotes the change of standard basis matrix with…

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: Suppose that T() and 7 () -E Find the standard matrix A for Tand find T(:) 14 and 2 and T (HD A-3…

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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: Get a base for your null space. Indicates which dimension it is in. The matrix is shown in the…

A: Step 1:

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

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Q: Consider the linear map T : Rª →→→ R¹, x→→→→ Ax, where [0 2 0 1 2 1 For which a is T one-to-one? A…

A: The given matrix,The aim is to find the values of  for which the linear map  is one-to-one.

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: Find a basis for the null space of the matrix 2 -2 -1 ( 1 -1 2 5 -5 0 A = 1 -1 1 5 3

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Q: Find a basis for the kernel of the matrix A. 1 2 -1 1 A = 3 1 2 1 -3 2 -3 3 5 ELET -3 1 3 -3 -1 3 3…

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Q: 5. Find the function ax6 + bx5 + c which is closest to x on the interval [−1, 1]. Find an orthogonal…

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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: Find a basis for the null space of the matrix. Show All Your Steps. 2) [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: Let 1 0 4 1 0 1 0 0 0 2 -4 0 0 0 0 1 1 7 1 1 A = 2 8. -1 6 3 0 1 = B. -3 –1 -2 5 - 2 6 0 2 (a) Find…

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Q: 2. Evaluate: 0020 2020 10 002 0022 Do columns of this matrix form a basis of R4? .

A: Columns of this matrix will form a basis of R4 only if columns forms a linearly independent set…

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.