1.2.10 Show that if ad – bc # 0, then the linear system ах + by 3D е cx + dy = f has a unique solution. Hint: Consider separately the cases a # 0 and a = 0.

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Q: 10 -7 Let u = and v = Compute u • v, v · v, ||u|| and find the dis- 13 16 tance between u and v.

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Q: 5. Give an example of a matrix A such that im(A) is in R2 is spanned by the vector A = %3D

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A: The given question is solved below.

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Q: Linear Algebra

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A: It is given that the matrix A is A=3-2101621-3071 and T:ℝ4→ℝ3 such that Tx=Ax where x=x1x2x3x4.…

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A: The detailed solution is as follows below:

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A: Let T be a linear transformation from a vector space V then according to dimension theorem ,…

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A: Here, u→=103v1→=012v2→=410

Q: Use Cramer's Rule to solve for x2. xi + 2x2 +x3 = 2 3x1 – x2 - 2x3 = 7 X2 +x3 = -1

A: Here we have given one matrix and we have to find the value of x2 by using the Cremer’s rule.   Now…

Q: 3. Find each of the following for the vectors u = (а) и - v. (1,–2,3) and v = (0,4,–1). (b) ||u +…

A: (a) u=1,-2,3, v=0,4,-1u.v=1,-2,3.0,4,-1      =1*0+-2*4+3*-1      =0-8-3      =-11 (b) u=1,-2,3,…

Q: 1. a) Find all solutions of the linear system x1 + 2x2 + 2x3 +x4 = 14 -21 – 2x2 – 34 = -4 2x1 + 4x2…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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