Let the correlation matrix of XT = (X, X) be (1) Show that the matrix C...

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Let the correlation matrix of XT = (X₁, X₂) be (1) Show that the matrix C is invertible. Let I= c = (0.75 0,75). C 1 (1) be the identity matrix. (2) Let 2.2857 -1.7143 C-1 = (² -1.7143) 2.2857 Show that CX C-1 = I. Show your working (keep accuracy of your calculations to 4 decimal places). (3) The eigenvalues and the eigenvectors of Care A₁ = 1.75 x₁ = (1, 1) A2 = 0.25 x₂ = (-1,1). Verify that (C-₁1)x₁ = 0 and (C-λ₂1)x₂ = 0. Show your working. (4) Verify the relationship between the trace of matrix C and the eigenvalues. Let the correlation matrix of XT = (X₁, X₂) be (1) Show that the matrix C is invertible. Let I= c = (0.75 0,75). C 1 (1) be the identity matrix. (2) Let 2.2857 -1.7143 C-1 = (² -1.7143) 2.2857 Show that CX C-1 = I. Show your working (keep accuracy of your calculations to 4 decimal places). (3) The eigenvalues and the eigenvectors of Care A₁ = 1.75 x₁ = (1, 1) A2 = 0.25 x₂ = (-1,1). Verify that (C-₁1)x₁ = 0 and (C-λ₂1)x₂ = 0. Show your working. (4) Verify the relationship between the trace of matrix C and the eigenvalues.