Question: Determine whether the vector = = is in the kernel of the linear mapping defined by the standard matrix 3 -5 A = -5 5

Determine whether the vector = = is in the kernel of the linear mapping defined by the standard matrix 3 -5 A = -5 5 9 -12 -15 O r is in the kernel of the linear mapping O i is not in the kernel of the linear mapping Determine whether the vector = = is in the range of the linear mapping defined by the standard matrix A O is in the range of the mapping O Is not in the range of the mapping Determine if the linear mapping L: R3 _ R* defined by = 4x1 - 313 is injective or not. O The mapping is injective O The mapping is not injective Determine if the linear mapping L: R? _> IR defined by ()=[ 4r1 + 212 3:1 + 212 is surjective or not. O The mapping is surjective O The mapping is not surjective

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