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Most versatile solver for Linear Algebra problems. Easy to understand with step-by-step explanations. Powered by Solvely.

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Explain this linear algebra concept.
Determine if the vector \(v = (3, -4, 2)\) is in the span of the vectors \(u_1 = (1, 0, -1)\), \(u_2 = (2, -2, 3)\), and \(u_3 = (-1, 2, 4)\).
Find the projection of the vector \(a = (3, 4)\) onto the vector \(b = (2, -1)\).
Show that the transformation \(T(x, y) = (x + 2y, 3x - y)\) is a linear transformation and find the standard matrix for \(T\).