2. Let a, B, y be three vectors in the inner product space V½ (R) with the standard inner product defined on it and (a, Y) = - 1, (B, Y) = 3. If a= (1,2), ß=(- 1, 1)| %3D then find y.

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: 4. State with a brief explanation whether the following statements are true or false. (a) The…

A: a) true The vectors (1 ,0) and (0,1) is linearly independent. We know that linearly independent set…

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

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Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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

A: Null space, N(A) is the set of all vectors x in R^4 here, which are solutions of the equation Ax=0,…

Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

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Q: If it is known that the internal product of the vectors ā (4, x, -2) and ƃ (1, x + 1,5) is 6,…

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors <1,1,0> and <0,1,1> to get a cross product for a…

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

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Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: 3.- Define the vector that allows the linear combination and if it exists, demonstrate the linear…

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Q: Find two different combinations of the three vectors u = (1,3) and v = (2,7) and w = (1,5) that…

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Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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