MTH 141 Chapter Notes - Chapter 3: L(R), Row And Column Spaces, Augmented Matrix
1 Jan 2016
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Matrix mapping for any matrix a we define a function corresponding to a by for x er. L2 must be closed under scalar multiplication and is linear closed under addition closed under scalar multiplication, thus f is a linear operator. If proving that it is not a linear operator/ not in the subspace you need to give an example where it is not closed under addition/ scalar multiplication. Compositions it is the same as matrix m times matrix l. Rotations in the plane if the rotation is at x. A reflection in the x2 axis (y) for the matrix. As seen here, a reflection in the x1 (x) axis yields a negative value in x2. This answer is obtained by having a standard basis, and then placing the negative value into the matrix. Solution is obtained from the solution space of the corresponding homogenous problem (ex 1 ), just the addition of the [5,0,0] in x1.
