Which of the following is true for an inner product (u, v)? (u+v, w) = (u+w, v) (u, v) = (v, u) (v, v) = 0 for all v (cu, cv) = c(u, v) for any scalar c

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: Q2: (a) Find the scalar and vector projection of ū along ủ, where u¯=(2, 3, 4) and v¯=(2, 2, 0). (b)…

A: Given : u=2,3,4, v=2,2,0 we know that scalar projection of u along v is given by…

Q: Find a subset ofbthebvectors v1=(0,2,2,4), v2=(1,0,−1,−3), v3=(2,3,1,1) and v4=(−2,1,3,2)that forms…

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A: Linear transformation: Let us consider a mapping T:V→W defined as T(v)=w where v∈V and w∈W [  v is…

Q: Find the real values of ,a,b,c that make the convolution equal to zero for the vector function F(x,…

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Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

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Q: True or False: Given a function of two variables f(x, y), the vector Vf(a, b) is perpendicular to…

A: It is false. The gradient vector ∇fa,b is not perpendicular to the graph z=fx, y at the point with…

Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² +…

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Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

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Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

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Q: Consider the following function. T: R2 - R3, T(x, y) = (2x², 3xy, y²) Find the following images for…

A: Let us consider the given transformation T:V→W then the transformation is said to be linear…

Q: Find a vector-valued function whose graph is the plane x+y+z== a. r(u,v)=ui-vj-(3-u-v)k b. r(u,v)=…

A: The equation of plane x+y+z=3

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: Use the function to find the image of v and the preimage of w. T(Vg, V2) = (V, + V2 V1 – V2), v =…

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Q: - Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in…

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Q: Use the function to find the image of v and the preimage of w. T(V1, v2) = (Vị + v2, V1 - V2), v =…

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Q: Find a vector-valued function whose graph is the plane x+y+z= 12, O r(u, v)=-ui-vj+(12-u-v)k O r(u,…

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Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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