Let k be a positve real number and letA=⎡⎢⎢⎣2k−12√k2√k2√k1−2k−2√k2k−1⎤⎥⎥⎦ and B=⎡⎢⎢⎣−22k−12√k1−2k02√k−√k−2√k0⎤⎥⎥⎦. If det (adj A)+det(adj B)=106, then [k] is equal to[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k]

Let k be a positve real number and letA=⎡⎢⎢⎣2k−12√k2√k2�

1.	Let k be a positve real number and letA=⎡⎢⎢⎣2k−12√k2√k2√k1−2k−2√k2k−1⎤⎥⎥⎦ and B=⎡⎢⎢⎣−22k−12√k1−2k02√k−√k−2√k0⎤⎥⎥⎦. If det (adj A)+det(adj B)=106, then [k] is equal to[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k]
Answer» Let $k$ be a positve real number and let $A = ⎡ ⎢⎢ ⎣ \begin{matrix} 2 k - 1 & 2 \sqrt{k} & 2 \sqrt{k} 2 \sqrt{k} & 1 & - 2 k - 2 \sqrt{k} & 2 k & - 1 \end{matrix} ⎤ ⎥⎥ ⎦$ and $B = ⎡ ⎢⎢ ⎣ \begin{matrix} - & 22 k - 1 & 2 \sqrt{k} 1 - 2 k & 0 & 2 \sqrt{k} - \sqrt{k} & - 2 \sqrt{k} & 0 \end{matrix} ⎤ ⎥⎥ ⎦$ . If $det (adj A)+det(adj B) = 10^{6}$ , then $[k]$ is equal to $[$ Note: $adj M$ denotes the adjoint of a square matrix $M$ and $[k]$ denotes the largest integer less than or equal to $k]$