Let u, v, and w be vectors, and let a be a scalar. Prove the given property. (u + v) · w = u·w + v. w Let = (u1, u2), = (V1, v2), and w - (w1, w2). Then V = (lu1, u2) + (v1, v2)) · (w1, w2) ). (w1, w2) (u + v) · w = = U1W1 + V1W1 + %3D u1W1 + uzw2 + = (u1, u2) · ( (V1, v2) · %3D = u. W + v• w.

Q: Consider the following vectors. u (6, –5) and v = (9, 1) u + v = (12, – 3) | (c) Find 7v – u. 7v – u…

A: By algebra of vectors we solve the this question.

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A: Given Let Plugging the values in the equation:

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A: Given  T(v1,v2,v3) = (4v2-v1,4v1+5v2)Image of v is given by T(1,-2,-4) = (-9,-6) hence (a). the…

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A: Solution:-

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

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

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