Question: 2.6.5. Let T:RnRm be a linear transformation. a. If x is in Rn, we say that x is in the kernel of T if T(x)=0.

2.6.5. Let T:RnRm be a linear transformation. a. If x is

2.6.5. Let T:RnRm be a linear transformation. a. If x is in Rn, we say that x is in the kernel of T if T(x)=0. Show that if x1 and x2 are both in the kernel of T, then ax1+bx2 is in the kernel of T for all scalars a and b. b. If y is in Rm, we say that y is in the image of T if T(x)=y for some x in Rn. Show that if y1 and y2 are both in the image of T, then ay1+by2 is in the image of T for all scalars a and b

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