Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2x?, –1 +x+x², 1 – x + x²} , {1– 3r + 2², 1 – 3x – 2a², 1 – 2r + 32²} . B B' Find the coordinate matrices of p(x) = 9x²+4x – 2 relative to the bases B and B'. Verify that [x(p)]g' = PB¬B' [x(p)B].

Q: Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 +…

A: Here we will find matrix of linear transformation

Q: Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ +…

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Q: Let B = matrix from B to C 8 - { }], ] } and c-{[7], [43]} C = be two bases for R². Find the change…

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Q: Let T,(x1,x2) = (+4x1 – 5z2, +1æ1 – lz2), and T2(x1,X2) = (- 321 – 5æ2 , +5æı + 8x2). Write the…

A: To find the standard matrices for T1,T2 and T10T2.

Q: Find the 2 x 2 matrix P such that Pu is the orthogonal projection of in R² onto the line consisting…

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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: Compute 3P and 2Q. If the scalar product is not defined, state how you know. (a) 3P = 3. (b) 2Q = 2.…

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Q: If scalar multiplication and addition is redefined on R² in the following way, show that it is NOT a…

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Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Let X ∈ R3 be some xed vector with coordinates X1, X2, X3. Consider the action on vectors of the…

A: From the given information we get:

Q: Let B = {bj, b2} and C = {c],c2} be bases for a vector space V, and suppose bj 3 бс1 — 2с, and bz —…

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Q: Find the standard matrices A and A' for T = T₂ o T₁ and T' = T10 T₂. T₁: R² R², T₁(x, y) = (x − 3y,…

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Q: 5.6. Are the polynomials 1-2x+3x², 2+x-x², 1-2x+x² linearly independent in the vector space P₂? If…

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Q: Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) # (v1, v2) :=…

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Q: Which of the following sets are closed under scalar multiplication? (i) The set of all matrices in…

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Q: I have performed the following polynomial multiplication in matlab on two vectors of polynomial…

A: Since matlab is mymult=conv(v1, v2) and result is mymult=3 45 -6 -78 99 65 -54 -12 -10 240

Q: 3 Let M₂(R) be the vector space of all 2 × 2 matrices with entries from R. Show that M₂ (R) = W₁ W₂,…

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Q: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

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Q: Consider the following quadratic form; F(x, y, z) = 5x? + 2y? + 4xy + xz

A: Symmetric matrix

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

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Q: Consider two bases B = {b1,b2} andC : such that bị = cq – 4c2 and b2 = 6c1 – 5c2. Find the…

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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.