[M] Let H Span {v1, v2} and B = {v1,V2}. Show that x is in H and find the B-coordinate vector of x, for 14 19 -5 -8 -13 V2 10 13 18 10 15 ||

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: Find vector c × (a + 3b), where a, b, and c are given below. ijk i j k -1 a = 509,b=0 0 1 0 -9i+27i…

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Q: IP IE Express the vector + =[] y as a linear combination of = [2] -[1] and y=

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Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

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: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: }] respectively. Let y = and u = . Write y as the sum of two orthogonal vectors, y, in the span of…

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Q: Let vv be the set of all vectors of the form -a b vectors u and in R³ such that W = span{u, v}. ū =…

A: Given space W =

Q: -4--|--| 9. Find the norm vector of the vectors a =

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Distance = 4.41

Q: = ---- -2 8 span of v₁ and v₂? Let V₁ = and y = -5 -3 For what value(s) of h is the vector y in the

A: The given vectors  and .The objective is the find the value of  for which the vector  in the span of…

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

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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: For v = (l, 0) and w = (0, 1), describe all points cv with (1) whole numbers c (2) nonnegative…

A: Consider the vector: v=1,0. So, this is a vector along x-axis. (1) Let c be a whole number. So, the…

Q: Find the length of the vector v = (9, 3, 9). ||v|

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Q: Let u be a vector of length 3 in the direction of the positive y-axis and let v be a vector of…

A: Vector: - The term vector comes from the Latin word vector, which means "carrier." Vectors transport…

Q: Determine the is a non-negative integer

A: The number of non-negative integer solution to the vectors…

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: For any vector v = (a, b, 0), where a and b are any nonzero real numbers, Select one: True False vok…

A: Here I have written the notion, I have used in my solution

Q: Le and ü .Write j as the sum of two orthogonal vectors, a, in Span {u} and i2 orthogonal to ū.

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: and .We have to find .

Q: - 16] [1] Determine whether the vector v =| 17 |is spanned by the vectors and | 2 or not. 18

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Q: Let L₁ be the line passing through the points Q₁(-4, 5, −5) and Q₂(−1, 6, –2 and let L₂ be the line…

A: This is a question of 3D geometry and vector analysis.

Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.