Find the constants c1 and c2, such that vector < 1,7 >= c1 < 1, 2 > +c2 < 2, -1 >

Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Find the length of the vector.v = (4, 3)

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Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

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Q: Determine whether the set of vectors is orthogonal. 4 2 - 4 -4 - 3

A: To determine Whether these sets of vectors are orthogonal or not.

Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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Q: Find all vectors v such that xv =.

A: Given: 1,2,1×v=3,1,-5 We have to find all the vectors v such that the given equation is satisfied.

Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Determine if the vector 2 b -A = 3 5 can be written as a linear combination of the vectors ---- 1…

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Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Write the vector (1, 2, –1) as a linear combination (if possible) as of the vectors (-1,2, 1), (2,…

A: Solution: The objective is to determine whether the given vector is linear combination of the given…

Q: Determine if the vectors are linearly independent or not

A: The vectors are linearly independent.

Q: Show that the vectors are orthogonal.

A: Given vectors are u=&lt;u1, u2&gt;=&lt;4, -1&gt;v=&lt;v1, v2&gt;=&lt;2, 8&gt;

Q: Give an example of vectors in R^3 that spans R^3. (show works)

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Q: Find a vector in the same direction as (3, –2) with length 10.

A: The vector that has the same direction as 3,-2 has the coordinates proportional to the given vector.…

Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: Find all orthogonal vectors to u=(2, -3).

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Q: Find the length of the vector. v = (4, 3) Ilv|| =

A: The given vector is                               v=(4, 3) We have to find the length of the vector…

Q: Determine the tail of the vector whose head is (3, −2, 2).

A: We have to determine the tail of the vector whose head is 3, -2, 2 and position vector is: 24-1 We…

Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

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Q: Determine whether the vector v is a linear combination of the remaining vectors. v = 3

A: (1).  The given vectors are: v→=12 ,  u1→=-1   3    and    u2→=   2-3

Q: Find the length of the vector.v = (2, 0, −5, 5)

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Q: Find the length of the vector. v - (9, 12)

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Q: Express the vector x as a linear combination of the u's. U₁ = 0, U₂ = 5, -1.4 U3 Ox=-3u₁ +4u2 +243…

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Q: Determine which sets of vectors are orthogonal.

A: Given,

Q: Let a, b, and c be three-dimensional vector5. Identify whether the expression ax (b x c) will result…

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Q: Determine if the given vectors are linearly independent or linearly dependent.

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: u

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Q: Find the length of the vector v = (10, 1, 5).

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Q: Determine whether the vector v = 8 is spanned by the vectors and 3 or not.

A: Given three vectors and we have to find if  v=789 is spanned by111 and 123

Q: - Find the length of the vector -3v if v = (2, 3, -2, 1).

A: Givenv=(2,3,-2,1)-3v=(-6,-9,6,-3)

Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: The number of elements in a vector generated by [4:0.1:13] is

A: We have to find the number of elements in a vector generated by  [4 : 0.1 : 13].

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Find all vectors orthogonal to 3

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Q: .3

A: Given: v={ √2,3√2}

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: Express the product Ax as a linear combination of the column vectors of A. 1 21 3 + 3 +3 2.

A: The given product, A2×2x2×1=12-3432 Which will result into a vector of order 2×1

Q: Prove that two vectors are linearly dependent (taken as a set of vectors) if and only if one vector…

A: Let X and Y be two vectors. Suppose these two vectors are linearly dependent. [To prove: One vector…