Let, T: R²³ R³T (x₂√, z) = (x+√+2, 27¹², 24+32) • Test whether the transformation linear or not T is b Find the basis and dimension of Im T

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: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

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Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: Does V {x2 + x, 1 + x + 2x³, x3 2x, x + 3x²} span P3? Is it linearl- - independent? Is it a basis of…

A: That's easy. Have a good day!!!

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: Let s = {1, 2, 3} andT: Fun(S) + R' be the transformation T) = (10), s) – 2/), 1() – 12) and…

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Q: Give the coordinates of the harmonic conjugate of (–1, –1, 0) with respect to (1, 1, 1) and (3, 3,…

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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: (d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector…

A: Using 1+2x-x^2=ap1+bp2+cp3 find a b c

Q: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

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Q: True/False: If A is diagonalizable, then so is AT.

A: A matrix is said to be diagonalizable if a matrix of n×n elements has n linear independent eigen…

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: Let V be the plane with equation x-2x - 4x = 0 in R. Find the matrix A of the orthogonal projection…

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Q: linear operator T: P,P2 4. Cet the be defined by T(aotq, Xfayxtagx?)=3ast (az-93)x² a) Find a basis…

A: The given linear operator is                                               T : P3→P2 which is…

Q: Assume that: U1= -1 -1 u2= 1 And W=span {U1, U2}. -Find a basis to W-.

A: Here   u1 , u2 are two vector. W= span {u1, u2 } So, {u1 , u2 } is a basis . Now we found a basis ,…

Q: Find the dimension and a basis of U = r2s+t 0 -3r s-t r, s, tER

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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: Let ū = -4î + 4ĵ – 3k and i = î – 25 + 2k. (a) Let w = proj, ū. Compute w. (b) Compute u-w and show…

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Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: Define T : R? → R by 7((x, y)) = x+y. Describe the kernel of and fibers of T geometrically.

A: The kernel is a line with slope -1 and passes through the origin.

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

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Q: Find the vecctor projection of u=bi+3jtak onto Vzi-zj-2k and the scalar component of u in the…

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Q: im(T1 + 14T) im(14T† + T2).

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A: The null space of T is the collection of all polynomials p(x) in the domain of T such that T(p(x)) =…

Q: Consider the basis B of R2 consisting of vectors [2] and [2] Find in R² whose coordinate vector…

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Q: Without using determinants, show that {(2, –x,,3x²,x³} is a basis for Ps then find dimension for P3

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Q: = Consider the basis B₁ = {(1, 0, 0), (1, 1, 0), (1, 1, 1)} of R³ and the basis B₂: – 2), (3, -1)}…

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