Problem #12 Part A) Prove that C = { 1 + x + x²₁ 1+ 2x, is a basis for 1R₂ [x] Part B) Consider another basis B = {1, x₁ x ² } for Ra[x]. Find the change of basis matrix from C to B. Part C) Find the coordinate vector of x with respect to C. That is, find [x]c -x+ 2x²3

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A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

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A: We have to answer the following for the given maps.

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Q: please explain part d because i am confused by the second and third part of part d.

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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Q: 1 3 1 2 A=2 6 4 002 4 I= I Y Z ພ () and 6 = 3

A: Solution to the system

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A: Given:u1​=[2−6​],u2​=[124​],x=[2−2​]  Step 1: Check OrthogonalityTwo vectors u1​ and u2​ are…

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A: The standard basis B for M22 is {e1,e2,e3,e4}.