Write N(A) as the span of a vector (r vectors). What is dimN(A)? Why?

Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

Q: How do you know what the vector b is?

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Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: What is the zero vector?

A: We have to define

Q: Ex Look at the fixed point (1,11 of [x = x-y lý -1-xy Jacobian: J(x, y) = (y _x) J(₁, 1) = (1 - 1)…

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Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: ( E)i+(G + log(vF –1 – 1) + (5ť² +1 – log t)k |3 – V7 – t2| t2 – t – 1 T(t) =

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Q: Find the point on the line T = (-2, 2, 3) + t(4, 1, 1) that presents the shortest distance to the…

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Q: y 3 2 1 O -1 -2 -3

A: Given query is to find the x component of the vector.

Q: 6. Find the following. a. Find the B-coordinate vector of s(t) = 4+5 sin?(t) given B = {1, sin(t),…

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Q: 1 7(t) = Vt + 8

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Q: - Given the points A: (0,6,2) and B: (-5,-4,6), find the vector u AB

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Q: how can i learnd about vector in r2 and r3?

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Q: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

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Q: Give the  3 characteristics of a vector

A: Three Character of vectors are given:

Q: How are vectors added and subtracted geometrically? Algebraically?

A: Vector Addition Geometrically:

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: Verify that the vector functions?

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Q: 9. lul 4,0: Ju] 4,0 310°

A: Given query is to find the vector.

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: Find two linearly independent vectors perpendicular to the vector 15 "I G.

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Q: (b) Example: Are the vectors; v₁ = dependent? (1,-1,0)), v₂ = (1,3,-1) and v3 = (5,3,-2) linearly

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

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Q: Prove the Sum and Difference Rules for vector functions.

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Q: What is (A - B) and |A - B| * A = i + 2j – k, B = -2i + 3j + k |

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