b) Let T: R R2 be a linear transformation with its standard matrix given by 67...

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b) Let T: R² R2 be a linear transformation with its standard matrix given by 67 ($ 7). 32 You are told that the eigenvalues and corresponding eigenvectors of this transformation are { ( 7₁ ) | 1€ R₁1 +0} 31 B = A₁9₁ €₁= A₂ = -1, 4-{(7) PERAWD} 1+0} (i) Find a basis B3 for R² such that the matrix for T relative to B is diagonal. (ii) Find a diagonal matrix D which is the matrix for T relative to the basis B. b) Let T: R² R2 be a linear transformation with its standard matrix given by 67 ($ 7). 32 You are told that the eigenvalues and corresponding eigenvectors of this transformation are { ( 7₁ ) | 1€ R₁1 +0} 31 B = A₁9₁ €₁= A₂ = -1, 4-{(7) PERAWD} 1+0} (i) Find a basis B3 for R² such that the matrix for T relative to B is diagonal. (ii) Find a diagonal matrix D which is the matrix for T relative to the basis B.