The column space of each matrix A and B below determines a plane in R. We...

 

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The column space of each matrix A and B below determines a plane in R³. We will find a non-zero vector in the intersection of the two planes, i.e., a vector v in C(A) nC(B). 1 2 13 B 6 3 5 1 2 We want to find v so that v = Ax and v= By for some x and y. 7/1 (a) Let x = and y 2 Y2 a 3 x 4 matrix system with variables 71, 72, 7/1, and 1/2. Rewrite the equation Ax = By as (b) Find the complete solution to the system in part (a). Note that this should be the null space of the combined matrix [A |-B]. (c) Take a non-zero solution to the system from part (b) and split it into an x-part and a y-part. This should give you vectors x and y with Ax = By. D (d) Find a non-zero vector v in C(A) nC(B). The column space of each matrix A and B below determines a plane in R³. We will find a non-zero vector in the intersection of the two planes, i.e., a vector v in C(A) nC(B). 1 2 13 B 6 3 5 1 2 We want to find v so that v = Ax and v= By for some x and y. 7/1 (a) Let x = and y 2 Y2 a 3 x 4 matrix system with variables 71, 72, 7/1, and 1/2. Rewrite the equation Ax = By as (b) Find the complete solution to the system in part (a). Note that this should be the null space of the combined matrix [A |-B]. (c) Take a non-zero solution to the system from part (b) and split it into an x-part and a y-part. This should give you vectors x and y with Ax = By. D (d) Find a non-zero vector v in C(A) nC(B).