Let A be an
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- Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.arrow_forwardProve part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix over. With as defined in the preceding paragraph,arrow_forwardLet A and B be square matrices of order n over Prove or disprove that the product AB is a diagonal matrix of order n over if B is a diagonal matrix.arrow_forward
- In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem 5.2 to express was a linear combination of these basis vectors. Give the coordinate vector[w] ofwwith respect to the basis ={v1,v2}of 2or =v1,v2,v3 of3. v1=[111],v2=[110],v3=[112];w=[123]arrow_forwardFind a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.arrow_forward
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