2. (a) Find the general solution of the matrix equation Ax = 0, where [2 1 1] A = (b) Use the subspace theorem to show that the solution set you found in (a) is a subspace of R³. (c) Specify the vector form the line {(x, y, z) : 2x +1= }y -1 = z}. Show that this line is not closed under vector addition.

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Q: .

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Q: 2.14. Prove that two subspaces V1 and V2 are linearly independent if and only if Vịn V2 = {0}.

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A: The solution is given as

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Q: 3 Find a basis of the subspace of R' defined by the equation -7x1 – 5x2 – 4x3 = 0.

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Q: 1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes,…

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A: Use the given information.

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Q: 7. Find an orthonormal basis for the solution space of the following homogeneous system of linear…

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Q: Consider the system of equations on R² -x Y – 4x³ . 1. Find stable and unstable subspaces.

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Q: Let A be an mxn matrix. Prove that W = {x ER" | Ax = 0} is a subspace of R", where W is the solution…

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Q: 7. What happens if we apply the Gram-Schmidt process to a linearly dependent set of vectors? 8. Find…

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Q: • Consider the slope fields and the systems of the form y' = Aỹ, where A is given below. Match each…

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Q: Consider the system of equations on R2 y – 4a3. . Find stable and unstable subspaces.

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Q: 1. W is the set of all 2x2 matrices of the form 0 a where a and b are real numbers. Does W 3 b form…

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