Which of the following sets are subspaces of R³? A. {(x, y, z) |2x - 8y + 3z = 9}| □ B. {(−5, y, z) | y, z arbitrary numbers }| □ C. {(-9x, —2x, 8x) 1 x arbitrary number}| □ D. {(x, 0, 0) 1 x arbitrary number}| □ E. {(x, y, z) | - 5x + 4y +7z = 0}| □ F. {(x, y, z) | x

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: Use the change of variables X1 X2 X3 X4 = = G(r, 01, 02, 03): = to compute the content of the 4-ball…

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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: 3. ID V = Find all real numbers t for (20 – t,4t – 4,5t², t²) are orthogonal. which u = (1,5t,-4t,…

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Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

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Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

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Q: 3x3 Define T:R → R² by T 12 xi + 6x2 Find a non-zero vector in the kernel of T.

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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: Is T linear? If Yes find KerT, where T(x1, x2, x3) = (x1+x3, x1-x3, x2 )

A: Given Tx1,x2,x3=x1+x3,x1−x3,x2 We have to show that T is linear and then find the KerT Let…

Q: find the point of intersection for the following 3 planes  x–2y+z+6=0 2x+y–z+2=0 2x+y+3z+2=0

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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 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: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: IS a function.. (b) Let R= {(x,y) € R × R : 1 < ¤ < 4 or x = 6}, %3D and S = {(x, y) E R × R : –1 <…

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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: Supposer is an invertible function with domain [1, 5] and range [2,7]. Then the domain of r−¹(x − 1)…

A: Given that r is an invertible function with domain [1,5] and range [2,7].It means that for every…

Q: 2. (а) ở and w are vectors in R? such that f(0) = w. Express f(27 – 3w) as a linear combination of i…

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Q: Determine whether the following set of polynomials is linearly independent (1 – t)?, t – 2t2 + t³,…

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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: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A: Given that  where G,u and v are differentialblle functions

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: Find the degree of Q(V2, V5) over Q.

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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: u = [2, 6, –5] and v= [-3,–1,6] %3D A · A + (A + ng-) · (A x n)

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Q: Let u = = (–3, 3, 5) and v = (−6, −4, −7). Compute the following: ū X x v = v × x ū x ū ū=

A: Please note that as per bartleby guidelines, we need to answer only the first three sub-parts.Kindly…

Q: Suppose y E span{X₁, X₂}. Explain why span{x₁, x2, y} = span{X₁, X₂}.

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Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: [1030] Let A = 0 120 %3D V be the null space of A, and W= V.What is the dimension of W? 0 0 00 1 3.…

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Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: Let W (w1, w2, w3) = UxV (cross product) such that U(-3, 3, -3) and V(1, 1, 7) %3D find w2 Answer:

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Q: Solve A = -3 using the matrix inverse, given: %3D 1 -5 -1 2 [1 3 -21 A = 1 and A-1 = 0 1 %3D -3 1 [3…

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Q: Algebra IA-2. Logan Brockberg-Lesson 4 Homework.pdf Times New Roman 14px 1.5pt BIUS AA x, x…

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Q: Find all triples of integers (x, y, z) that satisfy x² + 2y² = z2.

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Q: Let u=2i+3j-2k and v=-1i-4j +k Find u . v, ||u|| and u . v

A: Given that u and v vector and we find its dot product (u.v) and mode of u(||u||). Here i attached…