Problem 1E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 2E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 3E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 4E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 5E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 6E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 7E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 8E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 9E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 10E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 11E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 12E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 13E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 14E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 15E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 16E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 17E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 18E: In Exercises 1 through 18, determine whether the vector xis in the span V of the vectors... Problem 19E: In Exercises 19 through 24, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 20E: In Exercises 19 through 24, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 21E: In Exercises 19 through 24, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 22E: In Exercises 19 through 24, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 23E: In Exercises 19 through 24, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 24E: In Exercises 19 through 24, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 25E: In Exercises 25 through 30, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 26E: In Exercises 25 through 30, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 27E: In Exercises 25 through 30, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 28E: In Exercises 25 through 30, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 29E: In Exercises 25 through 30, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 30E: In Exercises 25 through 30, find the matrix B of the linear transformation T(x)=Ax with respect to... Problem 31E: Let =(v1,v2,v3)be any basis of 3consisting of perpendicular unit vectors, such that v3=v1v2 . In... Problem 32E: Let =(v1,v2,v3)be any basis of 3consisting of perpendicular unit vectors, such that v3=v1v2 . In... Problem 33E: Let =(v1,v2,v3)be any basis of 3consisting of perpendicular unit vectors, such that v3=v1v2 . In... Problem 34E: Let =(v1,v2,v3)be any basis of 3consisting of perpendicular unit vectors, such that v3=v1v2 . In... Problem 35E: Let =(v1,v2,v3)be any basis of 3consisting of perpendicular unit vectors, such that v3=v1v2 . In... Problem 36E: Let =(v1,v2,v3)be any basis of 3consisting of perpendicular unit vectors, such that v3=v1v2 . In... Problem 37E: In Exercises 37 through 42, find a basis of n such that the matrix B of the given linear... Problem 38E: In Exercises 37 through 42, find a basis of n such that the matrix B of the given linear... Problem 39E: In Exercises 37 through 42, find a basis of n such that the matrix B of the given linear... Problem 40E Problem 41E: In Exercises 37 through 42, find a basis of n such that the matrix B of the given linear... Problem 42E: In Exercises 37 through 42, find a basis of n such that the matrix B of the given linear... Problem 43E: Consider the plane x1+2x2+x3=0 with basis consisting of vectors [101] and [210]. If =[23] , find x . Problem 44E: Consider the plane 2x13x2+4x3=0 with basis consisting of vectors [841] and [521]. If =[21] , find x... Problem 45E: Consider the plane 2x13x2+4x3=0. Find a basis of this plane such that =[23] for x=[201] . Problem 46E: Consider the plane x1+2x2+x3=0. Find a basis of this plane such that =[21] for x=[111] . Problem 47E: Consider a linear transformation T from 2 to 2 .Weare told that the matrix of T with respect to the... Problem 48E: In the accompanying figure, sketch the vector x with=[12], where is the basis of 2 consistingof the... Problem 49E Problem 50E: Given a hexagonal tiling of the plane, such as you mightfind on a kitchen floor, consider the basis... Problem 51E Problem 52E: If is a basis of n , is the transformation T from n to n given by T(x)= linear? Justify your answer. Problem 53E: Consider the basis of 2 consisting of the vectors [12] and [34].We are told that=[711] for a certain... Problem 54E: Let be the basis of n consisting of the vectors v1,v2,...,vn,and let be some other basis of”. Is a... Problem 55E: Consider the basis of 2 consisting of the vectors [11] and [12],and let be the basis consisting of... Problem 56E: Find a basis of 2 such that and Problem 57E: Show that if a 33 matrix A represents the reflection about a plane, then A is similar to the matrix... Problem 58E: Consider a 33 matrix A and a vector v in 3 suchthat A3v=0 , but A2v0 . a. Show that the vectors... Problem 59E: Is matrix [2003] similar to matrix [2113] ? Problem 60E: Is matrix [1001] similar to matrix [0110] ? Problem 61E: Find a basis of 2 such that the matrix of the lineartransformation T(x)=[5947] is B=[1101] . Problem 62E: Find a basis of 2 such that the matrix of the linear transformation T(x)=[1243]x is B=[5001] . Problem 63E Problem 64E: Is matrix [abcd] similar to matrix [acbd] for all a, b, c, d? Problem 65E: Prove parts (a) and (b) of Theorem 3.4.6. Problem 66E: Consider a matrix A of the form A=[abba] , where a2+b2=1 and a1 . Find the matrix B of the linear... Problem 67E: If c0 ,find the matrix of the linear transformation T(x)=[abcd]x with respect to basis [10],[ac] . Problem 68E Problem 69E: If A is a 22 matrix such that A[12]=[36] and A[21]=[21] ,show that A is similar to a diagonal matrix... Problem 70E: Is there a basis of 2 such that matrix B of thelinear transformation T(x)=[0110]x is upper... Problem 71E: Suppose that matrix A is similar to B, with B=S1AS . a. Show that if x is in ker(B), then Sx is in... Problem 72E: If A is similar to B, what is the relationship betweenrank(A) and rank(B)? See Exercise 71. Problem 73E Problem 74E: Consider the regular tetrahedron in the accompanying sketch whose center is at the origin. Let... Problem 75E Problem 76E Problem 77E Problem 78E: This problem refers to Leontief’s input—output model, first discussed in the Exercises 1.1.24 and... Problem 79E Problem 80E Problem 81E: Consider the linear transformation T[x1x2x3]=[x2x3x2+x3] from 3 to 3 . a. Find all vectors of the... 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