16. Let us consider V = C² with the Euclidean inner product. Let us consider the linear T₁, T2, T3, T4 which have the following matrices in the standard basis transformations ^2 = (-²₁ 1). ^s = (-³₁1)₁ 4 = (18) A₂ A3 A4 -i 4₁ - (²11) = i For all j = 1, 2, 3, 4 answer the following questions: • Is T; normal? • Is T; self-adjoint? • Is T; unitary?

Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

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