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- Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). Show that the system Ax = b must be inconsistent.Get a base for your null space. Indicates which dimension it is in. The matrix is shown in the image.If u and v are orthonormal vectors, show that P = uuT + v vT is the standard matrix of an orthogonal projection onto span (u, v). [Hint: Show that P = A{ATA)~1AT for some matrix A.]
- Let Eki be the elementary matrix formed by subtractingα times the ith row of the identity matrixfrom the kth row. Show that Eki = I − αekeTi .Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y, z, x) to bring back (x, y, z).Find Vector production of b onto a a=(-3,4) b =(6,7)