Determine whether (u, v) = (u, u₁v₁, v2) is an Inner Product on R².

Q: The following table shows the weight of a person and the number of hour of exercise they do. Weight…

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Q: rewrite ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz+j=0 in  standard form by matrix

A: The objective of the question is to rewrite the given quadratic equation in three variables in…

Q: Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a…

A: Ggg

Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]   Find a non-zero vector…

A: Given matrix is A=-24-2-42-6-31-382-30253

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

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Q: Find an algebraic description of the range of A by row reducing A^T and using the relation between…

A: We know that rank(A) = rank(AT). We need to find an algebraic description of the range of A by row…

Q: how can one show that three vectors span R^3?

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Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: Find each dot product and using properties of the Dot product 1) (3, 4 ) * (2 , -3) 2) (-3, -5) * (1…

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Q: Calculate the cross product. (9j - 5k) x (2j+ k) (Give your answer using standard basis vectors.…

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Q: 9) (Section 9.4) Find the magnitude of vector u = -60i+11j

A: Given,   u = -60i+11jMagnitude of vector ; u=-602 + 112u = 3600+121  = 3721 =61

Q: y²uxx - xyuxy - 2x² Uyy Find the canonical form of the equation. = 0, x > 0, y > 0

A: We have to find the canonical form of the equation.

Q: - (0·0-0-0) Is B: - a basis for R³? Explain how you know.

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Q: Find the basis of the solution space U of the equation x-y+z-w=0 of the form e_1=(a,1,0,0)…

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Q: (1, 0, 0), (1, -1, 1), (2, 1, 3), (1,1,1) are not bases of R^3. Can you explain why they are not?

A: Explanation:To form a basis for R^3 , we need exactly 3 vectors that are linearly independent and…

Q: The vectors (attached) form a basis of R^3 (R = Real numbers) if and only if k does not equal blank

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Q: determine whether (1, -3, -3) belongs to the span of {(1, -1, 1), (1, 1, -1), (-2, 2, -2)}

A: write all 3 vectors in the matrix A=11-2-1121-1-2 the vector b is b=1-3-3 if the system Ax=b is…

Q: Determine the following three vectors {, , } forms a basis for R^3. Expalain your answer.

A: Answer  Given  <2,1,0> , <4,2,2> and <-2,-1,3>  Let check whether they are…

Q: Consider a basis for a space given by vectors -5 0 -10 -4 2 -5 -10 0 -10 -2 6 0 Answer the following…

A: answer is in next step. please give a like!!!!

Q: 18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k

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Q: Determine if the set {(1,1, −1), (1, −1,1), (0,0,1)} is a basis of ℝ^3

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Q: matrix A and matrix B are defined in image calculate 3A-3B then find 6A^T

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Q: Compute the dot product (7, 6, 8) - (4, 10, 8).

A: To find - Compute the dot product 7, 6, 8·4, 10, 8

Q: Find projyu and projuv. Use the Euclidean inner product. u = (-1, 2, 1), v = (1, 2, –1) (a) projyu…

A: Given u = (-1, 2, 1) and v = (1, 2, -1)

Q: Vector Arithmetic Practice Compute: 15· (,-) – 32 ·(,-) =| | 24 - (,-) - 15 · (,-) =| -15-(금,-> -·…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…