Let A = -3 12 12 دن ته د -6 -6 -3 6 6 6 Find an orthogonal matrix P with rational entries and a diagonal matrix D such that D = P Г

Use the matrix P to determine if the matrices A and A' are similar. -1 -1 P=[11] 2 p-1 = 6 [2], 15 -20 -12 P-¹AP = 10 10 ==-₁-7] A' = ⁹]

Let the Matrix A =( 1 -2 -6 , 0 3 7 , 1 -2 5 ) and vector b = (11 , -5 , 9 ) is b in the span of the column space A ?

2 and u = 4 Write as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u. Let y = - 8 y=ý+z=D+0 (Type an integer or simplified fraction for each matrix element. List the terms in the same order as they appear in the original list.)