[M] Determine whether w is in the column space of A, the null space of A, or both, where -8 5 -2 2 -5 -2 A 10 -8 6 -3 3 -2

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 4, g(x) 2x, and h(x) = -x²,…

A: Sincewe can write every element of P2 in linear combination of f(x),g(x),h(x) so this functions…

Q: Use the sub no spaces: T-2y = - %3D 3x + 2y

A: Given that: x-2y=-10           ........(1)3x+2y=-14      ..............(2)

Q: Determine whether v is in the column space of A, or the null space of A, or both, or neither. -8 -2…

A: First, perform the row reduction to get the row reduction echelon form. Solve Ax=0 to get the…

Q: Prove that (a) C(B) C Nul(A), where C(B) denotes the column space of B. (b) rank A + rank B < 5

A: Given that A is a 3×5 matrix and B is a 5×6 matrix. Also AB=0.

Q: Determine whether w is in the column space of A, the null space of A, or both. 3 7 5 -6 3 1 A = 0 -4…

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Q: Find the absolute maxima and minima of the function on D, where D is the closed triangular region…

A: For finding the absolute maxima and minima values  Substitute the values of a vertices of a triangle…

Q: 9 T1, T2 are normal operators on an laner produce space with the property that either commutes with…

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Q: Use the functions f and g in C[-1, 1] to find (f, g), ||F||, ||9||, and d(f, g) for the inner…

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Q: Find the dimensions of the following linear spaces. (a) RSX3 (b) P6 (c) The real linear space C

A: In general Rm×n is a vector space of dimension m×n. So, Dimension of R5×3 is 5×3 = 15 (a) 15

Q: [M] Determine whether w is in the column space of A, the null space of A, or both, where 6. -1 -4 -1…

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Q: Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions…

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Q: Let V be the F-vector space of F-valued sequences

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Q: Find norm of the function in In Space L1 [o13 O a. 15/81 O b. 15/324 O c. 17/81 O d. 17/324 O e.…

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Q: Determine whether or not T = (6,-3) belongs to the null space of A' if A 1

A: the answer is

Q: Ex3 i) ii) Let T: C ([0,1]) → R f → f(0) If C ([0,1]) is equipped with the sup-norm, show that T is…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: Find the null space for A. 1 0 -2 A = 0 1 null(A) = span

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Q: .. .): P, is a polynomial space with degree with order n and less than equal n. Is the space S =…

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Q: Verify that the set C[a, b] of all continuous real-valued functions defined on the interval a ≤ x ≤…

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Q: Find a norm of the function f(t) =t – 2t in space L10, 1] 1 a. 6 С. е. d. ai

A: We use the definition of norm in L1[0,1] to answer the given question.

Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: (b) Show that the set of all positive real numbers, with x+y and cx redefined to equal the usual xy…

A: Here, to check that the set of all positive real numbers with  x+y=xy and cx=xc where xy is usual…

Q: Consider the inner product space (P2, (, )) with the inner product (p(x), q(x)) = p(0)q(0) +…

A: The inner product on the vector space of real polynomial of degree at most 2 ℙ2 is defined as…

Q: Find a norm of the function flt)= t+2t in space C^co13 %3D where normis given by formula ms x…

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Q: The set of all polynomials of degree † under the standard addition and scalar multiplication…

A: Suppose  P7=f(x) | f(x) is a polynomial of degree 7. Then we have to check why this set is not a…

Q: Find the dimension of the vector space.P4

A: Here the given vector space V= P4 or

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

A: For satisfying the inner product condition, function has to follow these three conditions: 1)…

Q: Either use an appropriate theorem to show that the given set, W, is a vector space, or find a…

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Q: b.) answer. Let f = x² and g = (1-x)². Are x and y orthogonal in this inner product space? Justify…

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Q: Are the following sets of functions, each defined on x € R, linearly independent? Use Wronskian. (a)…

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Q: Consider the collection of all points of the form y – 2w 3w Express this collection as the span of…

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Q: Let v= C[-1,1] What is the norm of the functionf(x) = - x in this space? O A) 2V5 O B) 2V10/5 OC)…

A: An inner product in the vector space of continuous functions in [-1, 1], denoted asV=C-1, 1, is…

Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

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Q: Use the functions f and g in C[-1, 1] to find (f, g), ||f||, ||g||, and d(f, g) for the inner…

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Q: Let P3 is the vector space of polynomials of the degrees3,Consider the polynomials…

A: Given :  P3 is the vector space of polynomials of degree less than or equal to 3. To prove :  We…

Q: 2. If T1, T2 are normal operators on an laner produce space with the property that either commutes…

A: Given that T1, T2 are normal operators of an Inner product space. So, T1T1*=T1*T1 and T2T2*=T2*T2,…

Q: Let P2(x) denote the set of all polynomials p(x) = ao+a1x+a2x² where the degree of p(x) is less than…

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

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Q: Let f be a function that takes elements of R?rR? into R' as follows: f(u, v) = |u1v1|+ |u2v2|, where…

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Q: Use the inner product (f, 9) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) in P, to find the orthogonal…

A: Vbb

Q: If p4 is a vector space formed by polynomials of degree less than 3 And  s = { ax^3 + bx^2 +cx + d…

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Q: Find a norm of the function f(t) = 2t4 – tin space C0, 1], where norm is given by formula max|f(t)|…

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

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Q: Consider the inner product space (P2, (,)) with the inner product (p(x), q(x)) = p(0)q(0) + p(1)q(1)…

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Q: Find isomorphic spaces O R and R² O P3 and M2x1 O P3 and M2×3 O P3 and R2 O R' and M2×2

A: We have to choose whether the given spaces are isomorphic or not.

Q: Verify that the set C[a, b] of all continuous real-valued functions defined on the interval a ≤ x ≤…

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Q: 7. Find the dimensions of the following linear spaces. (a) R2x7 (b) The real linear space C° (c) P3

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Q: Let f(x,y) = x - 5xy -y². Compute f(6,0), f(6, – 2), and f(b,c).

A: Solved below

Q: Use the functions f and g in C[-1, 1] to find (f, 9), ||f||, ||9|l, and d(f, g) for the inner…

A: Given that f,g=∫-11f(x)g(x)dx where f(x)=5x  and g(x)=e-x (a).…

Q: Show that the function defines an inner product on R2, where u = (u1, u2) and v = (v1, v2). ⟨u, v⟩ =…

A: Given function u,v=u1v1+9u2v2 where u=u1,u2 and v=v1,v2 The function is defined on R2. To show that…

Q: Qz\ show that ?_C=0} is not a swbopace of R

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