Mathematics

Problem

Let

C=\begin{pmatrix}m & 3\\ 5 & 7\end{pmatrix}

, where

m

is a real number. a. (i) Determine the condition on

m

that ensures

C

is invertible. b. (ii) For

m=4

, calculate only the element in the first row and second column of

C^{-1}

. c. (iii) Using your result from part (ii), verify that the first row of

C^{-1}C

equals the first row of the identity matrix.