For each subset of the xy-plane, decide if it is a subspace of R². The set of points where x = = 0. The set of points where y = 2. = 3. The set of points where x = The set of points where 3x = 2y. The set of points where y = 0. Subspace of R2 Not a subspace of R² Subspace of R² Not a subspace of R² Subspace of R2 Not a subspace of R² Subspace of R² Not a subspace of R² Subspace of R² Not a subspace of R²

Q: Let L₁ be the line passing through the points Q1=(-4, 2, -4) and Q2-(-1, 0, -6) and let L2 be the…

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Q: Let B = {(1,2,3), (3, 2, 1), (0, 0, 1)}. Show that B is linearly independent and spans R3. Show all…

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Q: Define linear dependence and independence of vectors. Examine for linear dependence [1, 0, 2, 1],…

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Q: Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T =…

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Q: Consider the set V of all vectors of the form (x y z)T where x, y and z are real numbers. 3. Show…

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Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

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Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

Q: Find the closest point to y in the subspace W spanned by v₁ and v2. y= 3 -1 1 16 V1 11 1 -4 1 5 V2 =…

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Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

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Q: Let u be a linear combination of {1₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} =…

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Q: -0-0-0-0 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the…

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Q: Let x = (13, −20, 15), v1 = (1, −2, 3), and v2 = (−1, 1, 1). Then the set {v1, v2} is orthogonal. It…

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Q: Find the dimension of the subspace spanned by the given vectors below. 4 6. -5 8 -4 O 3 O 4

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

A: Vector Subspace Test: A non-empty subset W of a vector space V is a vector subspace of V if and only…

Q: Let a, 1 1 -7 -7 3 and b = 3 15 h For what value(s) of h is b in the plane spanned by a, and a₂?

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Q: Which of the following sets is always linearly dependent? A set that contains the zero vector A set…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let V₁ = -4 1 | -12 B-B- V2 = 4 -3 11 -5 " and y = For what value of h is y in the plane spanned by…

A: and We have to find the value of .

Q: All computations must be shown. 1. Let pi(t) = 1+ t², p2(t) = t +t² and p3(t) = 1 + 2t + t² be…

A: Consider the provided question, given,p1t=1+t2p2t=t+t2and p3t=1+2t+t2

Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.

Q: Let 9 -15 ------ 12 V2 = -6 h = V1 = -3 3 1 - 2 For what value of h is y in the plane spanned by v₁…

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Q: , Y, 2, W) w) 3. Using methods of linear algebra verify whether Question a. span{(2,0,0), (1, 3,0)}C…

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Q: Let L₁ be the line passing through the points Q₁-(-1, -3, 1) and Q₂=(-4, -6, 2). Find a value of k…

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Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.