Issac O.

a) (A^−1+B^−1)^−1=A(A+B)^−1Bb) (A+BB^T)^−1B =A^−1B(I +B^TA^−1B)^−1

Show that for matrices 𝐴, 𝐵 ∈ ℝnxn, a vector 𝒘 = 𝐴𝐵𝒙 can be written as 𝒘 = ∑ni=1 (𝒃iT𝒙)𝒂iwhere 𝒃𝑖T is the 𝑖th row of matrix 𝐵, and 𝒂i is the 𝑖th column of matrix 𝐴.(Hint: Let 𝒛 = 𝐵𝒙, then 𝒘 = 𝑧1𝒂1... more

Compute the condition number of the following matrix to relative to ||.||infinityA=[1 -1 -10 1 -10 0 -1]