2. Consider the quadratic form Q : R° → R, where Q(x1, 22, x3) = –2x – 8x – 18x3+ 8x1x2 + 4x1x3 + 4.x2x3. Transform Q to canonical form and give the transition matrix, which transforms the natural basis into the canonical basis. Decide whether Q is definite.

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

A:

Q: Find the vector x determined by the coordinate vector [x]p in the given basis ẞ. B = -7] ,[x]ẞ = 9

A:

Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

A:

Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, -2+4t², and -12t+8t³; and let…

A:

Q: c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in…

A:

Q: Consider the vector v = 1 + 4t in terms of the standard basis for P2, {1, t, t²} and new basis B =…

A:

Q: Let B = 3 (1, x + 8, (x − 1)², 2x³) be an ordered basis for P3. Find the coordinate vector of 3 -…

A: fB​=[161, −19, −6, 4]Explanation:Detailed explanation:This is a detailed guide explaining how to…

Q: Let B = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

A:

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: Let: v = the matrix: -20 -15 11 18 Write v as a linear combination of the vectors in the following…

A:

Q: Let B, D be the following two bases of R³: -1 B = D= a) Find the change of coordinates matrix Po-s…

A: Solution is below.

Q: Let W be the set of all vectors of the form with r, s and t real. Find a matrix A such that W =…

A: To find matrix A such that

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

A:

Q: 3 Find the coordinates of y 7 relative to the orthogonal basis Uj = U2 = U3 = -2 -4 10 2 2 4 252

A: The solution is given as

Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

A:

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1, b2, b3}. 1 4 1 - 6 b, 0 ,…

A:

Q: E Let p 8x + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, Pi = 1,…

A: We have to find the coordinate vector of P.

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.