2 Express each of the following vectors in R² as linear combinations of the vectors [2] and (a) (b) (c) 13 [³] = || = N + 4 + + + + IC 5 3 5

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: For any two non-zero, non-parallel vectors ā and b, the vectors ā x b and (2ā + b) x (ā – b) are…

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Q: Find a vector orthogonal to both 7 -10 and w -10 -10 -4 7

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Q: -14 Given that write 3 -5 -3 -14 ] -5 = 2 -2 -3 1 0 0 −1 −1 as a linear combination of the vectors 1…

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Q: b) Determine the values of x so that the following vectors are linearly dependent. (1 3 3 -6 -x.

A: Using determinant property of linearly dependent vectors,

Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: (a) [1 2]. [–1 1] (c) [1 3], [2 – 3]. [0 2] (d) [2 4], [-1 2] (b) [0 0]. [1 1]. [–2 – 2]

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Q: Consider the vectors U₁ = 2x² + 2x - 1 and U₂ = -x² - 3x + 1 in P₂. Which of the following vectors…

A: Vectors v1=2x2+x-1 and v2=-x2-3x+1. To find the vectors that are linear combination of v1 and v2.

Q: Find a vector orthogonal to both = 10 2 and w = 2

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Q: Let v1 = (-6, -6, -9), i2 = (3, 3, 12), iz =(-1,-1,6). Are the vectors v1, 02 and vz linearly…

A: See the attachment

Q: 6. Prove that A ·B+ |A x B|< 2|A||B|| for arbitrary vectors A, B and C.

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Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: For the vectors A = ux + 3uy + 5uz, B = 2ux + 4uy + 6uz, and C = 3ux + 4uy + 5uz, show that A × ( B…

A: For the given vectors A,B,C show the given property  If A=a1ux +a2uy+a3uz and B= b1ux+b2uy+b3uz then…

Q: Given the following vectors A = -4a +3a-2a₂ X y B=a_+5a +7a_ X y z C=-2a-4a +6а X y Evaluate |AX…

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Q: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

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Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

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Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

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Q: T: P2 P₂ defined by T(a + bx + cx2) = a + b(x + 8) + b(x + 8)² Find the following images of the…

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Q: 9. Find all real values of c such that the vectors and +3 are linearly independent.

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

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Q: Compute the quadratic form x Ax for A= Xx₁ 12 - a. x = b. x= 1 X2 a. x¹Ax= 3 2 [1] 10 C. X = and…

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Q: Let x, y, z be (non-zero) vectors and suppose that z = -1x + 1y and w = -1x + 1y - 3z. Are the…

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Q: Describe the solutions of x1 + 2x2 – 3x3 = 5, 2x1 + x2 – 3x3 = 13, and –x1 + x2 = -8 %3D in…

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Q: Let a = 1 and b= 0 1 - What is |a|2|b²+la.b|²? be two vectors.

A: Concept: By using the symbol v, the magnitude of a vector formula can be utilized to determine the…