1. (a) Show that if BTA is nonsingular, then Po = A(BA)-BT is a projector. (Note:...

 

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1. (a) Show that if BTA is nonsingular, then Po = A(BA)-¹BT is a projector. (Note: Unless R(B) = R(A), Po is generally an oblique projector.) 1 1 For the parts that follow, let A = 0 1 3 2 and B = 1 (b) Calculate (by hand) the orthogonal projector PA onto R(A) (the range of A) as defined in the class notes. (c) Calculate (by hand) the projector Po defined in part (a). (d) Given your projectors in part (b) and part (c), determine the image of x = [1 2 3] under each of the following projectors: i. PA ii. (I-PA) iii. Po iv. (I-Po) 1. (a) Show that if BTA is nonsingular, then Po = A(BA)-¹BT is a projector. (Note: Unless R(B) = R(A), Po is generally an oblique projector.) 1 1 For the parts that follow, let A = 0 1 3 2 and B = 1 (b) Calculate (by hand) the orthogonal projector PA onto R(A) (the range of A) as defined in the class notes. (c) Calculate (by hand) the projector Po defined in part (a). (d) Given your projectors in part (b) and part (c), determine the image of x = [1 2 3] under each of the following projectors: i. PA ii. (I-PA) iii. Po iv. (I-Po)

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1 a a To show that PABBT A1BT is a projector we need to verify that it satisfies the two conditions ... View the full answer