Let u be some nonzero vector in R", L Span(u), and T(x) proj,(x) a) Prove that T is a linear transformation b) For any z E L, what is T(z)? Explain e) If A is the standard matrix for T, what does the result of part (b) tell us about the eigenvalues, eigenvectons, and/or eigenspaces of A?

Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

Q: Let T:V - V be the transformation whose matrix relative to basis {b1, b2, b3} is [x 3 -5 [T]B = y 7…

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Q: BLet uj = (1,2, 1), u2 = (2, 5, 2), u3 = (4, 8, 5). a) Find the transition matrix corresponding to…

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Q: Basis Find a basis for the space of 2 x 2 lower triangular matrices.

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Q: 3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 – i)a + 7b) (a)…

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Q: Consider the bases v₁ = (1,0)¹, v₂ = (0, 1) and v₁ = (2, 1), v₂ = (1,3)¹ of R². The transition…

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Q: Let T and T2 two linear transformations from R? to R², defined by 7(;) - ) ()-() 3x - 2y (;) (; x+ y…

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B =…

A: We will use the definition of inner product and Orthonormality of B

Q: Let T and T2 two linear transformations from R? to R², defined by (;) (C :(;) - (*:") . Зх — 2у x +…

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