→ R? and L(x) = (2x1 – x2, x2 +x3). Determine the Find the kernel of L, ker(L) where L: R3 dimension and the basis of ker(L). %3D

Q: Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) = x" Ax sa} + 3.x3 +…

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Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1)…

A: Given  be the set of all pairs  of real numbers together with the following operations:

Q: Let T R² R² be the linear operator defined by - x2 T([22]) = [ 91 +22] and let B = {u₁, u₂} be the…

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Q: Consider the basis B = {t^2 −2t+1, 4t^2 −5t+3, 3t^2 +2t} for P2. Compute (2t−1)B by setting up and…

A:

Q: Let S P₂ P₂ be the linear transformation where S(x) = -16x - 36 and S(1) = 6x + 14. -4 0 Suppose MB…

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Q: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

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Q: ) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1,…

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Q: For a 4×4 matrix whose top three rows are arbitrary and whose bottom row is (0, 0, 0, 1), show that…

A: Suppose our matrix is

Q: Let TA : R → R³ be multiplication by the orthogonal matrix 1 21 3 3 3 6- 1 Find TA(x) for the vector…

A:

Q: The vectors p1(t) = 1 + t², p2(t) = −t + 3t², and p3(t) = 1+t+t2 form a basis B 2(t), p3(t)} for…

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Q: Find the decomposition a = a + a₁ with respect to b if a = (3,4,2), b = (3, 4, 6). ab = (a||x, a|ly,…

A: Given: a→=3,4,2and b→=3,4,6 To find: Decomposition a=a∥+a⊥with respect to b. Here,…