Exercise 4 The set B = is a basis for the subspace U = {(x, y, z) | 2x – 3y– z = 0}. 1. U is either a line or plane. Which one is it? 2. Is B an orthogonal basis? If not, use the Gram-Schmidt algorithm to find an orthogonal ba for U. 3. Find U-.

Q: iii) The area of the parallelogram spanned by the three-dimensional vectors 3 -4 and 2 -5 is Number

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Q: Assume that A is row equivalent to B. Find bases for Nul A and Col A. - 2 8 -2 - 8 10 8 11 A = 2 -…

A: The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero

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A: Ggg

Q: O Find a vector orthogonal to both (-2, 1, 0) and to (0, 1, –5) of the form

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Q: how can one show that three vectors span R^3?

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Q: 5 et L be the line given by the span of in R³. Find a basis for the orthogonal complement Lt -7 -9…

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Q: I've been given that this is false. Can you please explain why this is false?

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Q: Find a vector v in space that has the magnitude ||v|| = 1/₁0 cos(a) > 0, cos(B) = cos(y) = and…

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Q: vecterd (l,l.3) .c2.3.6] a (libis) form Do the budia fer R?

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Q: Let e1, e2, e3, e4, ē5, e6} be the standard basis in R°. Find the length of the vector * = 471+…

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Q: Activity 2: A spherical tank is used to hold water as shown below. The volume of water in tank can…

A: The given equation that computes the volume of the water in the tank isHere V is the volume of the…

Q: Is it true that there is a basis for R^4 that consists of five vectors?

A: False. First I recall you what is the definition of basis. set B of vectors in a vector space V is…

Q: need help on this question   given the basis B={[12],[25]} of R2.{"version":"1.1","math":"\mbox…

A: We have to find the change of coordinates matrix from the standard basisE=1,0,0,1 of ℝ2 to the basis…

Q: Using the Gram-Schmidt process, construct an orthogonal basis for V con- sisting of vectors with…

A: Let's denote the given vectors as , , and :v1=[122],v2=[110],v3=[1−15].1. Start with .2.…

Q: Find the vector x determined by the given coordinate vector [x] and the given basis B. 8= 6 -6 X =…

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Q: Given the ordered basis B=A₁ -1 0 -[5], 42 - [8 A₂ -2 6 (4]} 8 16 -33 -1 3 [¹].4 A4 0 -9 A3 - find…

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Q: (1, 0, 0), (1, -1, 1), (2, 1, 3), (1,1,1) are not bases of R^3. Can you explain why they are not?

A: Explanation:To form a basis for R^3 , we need exactly 3 vectors that are linearly independent and…

Q: A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

A: Given statement is, “A set of three vectors in R4 spans R4.”

Q: Find a basis of Span((1,-1,3,0), (2, 1, -2, -1), (3, 3, -7,-2)).

A: We have to find a basis of Span ((1,-1,3, 0), (2, 1, -2, -1), (3, 3, -7,-2)).

Q: Find an orthonormal basis for the column space of 7 -11 1 -4 -1 0 2

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Q: 3) Let C be a basis that contains vectors (−2 + 1x + 1x2 + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 +…

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Q: The vectors (attached) form a basis of R^3 (R = Real numbers) if and only if k does not equal blank

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Q: ) Consider the vectors -- () --- () --- () a= = Do these vectors form a basis of R³? If yes, prove…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Determine the following three vectors {, , } forms a basis for R^3. Expalain your answer.

A: Answer  Given  <2,1,0> , <4,2,2> and <-2,-1,3>  Let check whether they are…

Q: Consider a basis for a space given by vectors -5 0 -10 -4 2 -5 -10 0 -10 -2 6 0 Answer the following…

A: answer is in next step. please give a like!!!!

Q: Determine if the set {(1,1, −1), (1, −1,1), (0,0,1)} is a basis of ℝ^3

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.