(We will use this exercise in the Matrix Inverses exercises.) Here is another property of matrix multiplication...
Question:
(a) Prove that the composition of the projections πx, πy: R3 → R3 onto the x and y axes is the zero map despite that neither one is itself the zero map.
(b) Prove that the composition of the derivatives d2/dx2, d3/dx3: P4 → P4 is the zero map despite that neither is the zero map.
(c) Give a matrix equation representing the first fact.
(d) Give a matrix equation representing the second.
When two things multiply to give zero despite that neither is zero we say that each is a zero divisor.
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