2题关于应用线性代数求解1.Supposeuandvarelinearlyindependentvectorsin¡n.Mustthe2vectorsu+v,u-vbelinearlyindependent?Explainwhyorwhynotbytakinglinearcombinations.2.Foreachofthefollowingdeterminewh

Question

2题关于应用线性代数求解
1. Suppose u and v are linearly independent vectors in ¡n . Must the 2 vectors u + v, u -
v be linearly independent? Explain why or why not by taking linear combinations.
2. For each of the following determine whether the transformation T is linear on nonlinear
using the definition. If it is linear, find a matrix A such that T(x) = Ax .
a) T(x1, x2)=(x1,x2,0)
b) T(x1,x2,x3)=(x1-3x2, x3, 1)
c) T(x1,x2,x3)=(x1,x2)

Answer 1

1.u+v,u-v,linearly independent.（u+v和u-v是线性无关的）.Suppose there exist two numbers a,b,（设存在数字a,b满足下式）.a*(u+v)+b*(u-v)=(a+b)*u+(a-b)*v=0∵ u and v are linearly independent,（因u和v是线...