If $A=\begin{bmatrix} 5a & -b \ 3 & 2 \end{bmatrix}$ and $A \cdot adj(A) = A \cdot A^{T}$, then $5a+b$ is equal to.

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Aicharya · Accepted Answer

Here's the corrected text with proper LaTeX formatting: $A=\begin{bmatrix} 5a & -b \ 3 & 2 \end{bmatrix}$ and $A^T=\begin{bmatrix} 5a & 3 \ -b & 2 \end{bmatrix}$ $AA^T=\begin{bmatrix} 25a^2+b^2 & 15a-2b \ 15a-2b & 13 \end{bmatrix}$ Now, $A \cdot adjA = |A|I_2 = \begin{bmatrix} 10a+3b & 0 \ 0 & 10a+3b \end{bmatrix}$ Given $AA^T = A \cdot adjA$ $15a-2b=0$ ......(i) $10a+3b=13$ .......(ii) Solving we get $5a=2$ and $b=3$ $	herefore 5a+b=5$

If $A=\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot adj(A) = A \cdot A^{T}$, then $5a+b$ is…

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