Question: 7. Consider the vector space of real-valued functions with basis (sinx, cosx). Show that (2sinx, 3cosx + sinx) is also a basis for this space.

7. Consider the vector space of real-valued functions with basis (sinx, cosx). Show that (2sinx, 3cosx + sinx) is also a basis for this space. Find the change of basis matrix in each direction. Show all your work.9. Find an orthonormal basis for the following subspace of R4: x y {z w M2y+zw=0} Show all your work. 2. Show that this matrix 1 O 1 1 -1 1 has infinitely many left inverses. Show also that it has no right inverse. Show all your work

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