Any two bases contain the same number of vectors. Let dim V = n. If you have n linearly independent vectors in V, prove that these span V.

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

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

Q: 3 Given that u = 4i+ GJ and Iv[ = 2, find vif u and V are or thugonal to each other.

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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: Determine the real value/s of c such that the following vectors are linearly independent: 4 - 2 -6 6…

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Q: Determine m such that the two vectors are orthogonal.

A: Given : 4mi+j and 9m-25j

Q: Determine m such that the two vectors are orthogonal.

A: The vectors 5mi^+3j^ & 2i^+7j^

Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: Find an explicit description of Nul A by listing vectors that span the null space.A = -6 4

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Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Let V1 MECANIS 3 1 11 V2 = 1 0 V3 = SCAMENTO 0

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Q: If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

A: Vector: An object which has both magnitude as well as direction is called a vector. We can draw a…

Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

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Q: Find nonzero vectors a, b, and c in space such that a × b= a X c but b# c.

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Q: If possible express the vector v as a linear combination of V1, V2, and V3.

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Q: Find all real values of c such that the vectors [2 and +3 are linearly independent.

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Q: Determine m such that the two vectors are orthogonal.

A: Given : 3i-2j and 4i+5mj

Q: 0 2 ))))( 0 4 1 0 3 0 1 2 3 4

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