ਕੋਈ ਵੀ ਗਣਿਤ ਸਮੱਸਿਆ ਹੱਲ ਕਰੋ

ਕਦਮ ਦਰ ਕਦਮ

1. \det A = 1

   A matrix is invertible only when its determinant is non-zero.

2. \left[\begin{matrix}1 & 2 & 3 & 1 & 0 & 0\\0 & 1 & 4 & 0 & 1 & 0\\5 & 6 & 0 & 0 & 0 & 1\end{matrix}\right]

   Gauss-Jordan: row-reduce [A | I] until the left block is I; the right block is then A⁻¹.

3. \left[\begin{matrix}1 & 2 & 3 & 1 & 0 & 0\\0 & 1 & 4 & 0 & 1 & 0\\0 & -4 & -15 & -5 & 0 & 1\end{matrix}\right]

   R3 ← R3 − (5)·R1 to clear column 1.

4. \left[\begin{matrix}1 & 0 & -5 & 1 & -2 & 0\\0 & 1 & 4 & 0 & 1 & 0\\0 & -4 & -15 & -5 & 0 & 1\end{matrix}\right]

   R1 ← R1 − (2)·R2 to clear column 2.

5. \left[\begin{matrix}1 & 0 & -5 & 1 & -2 & 0\\0 & 1 & 4 & 0 & 1 & 0\\0 & 0 & 1 & -5 & 4 & 1\end{matrix}\right]

   R3 ← R3 − (-4)·R2 to clear column 2.

6. \left[\begin{matrix}1 & 0 & 0 & -24 & 18 & 5\\0 & 1 & 4 & 0 & 1 & 0\\0 & 0 & 1 & -5 & 4 & 1\end{matrix}\right]

   R1 ← R1 − (-5)·R3 to clear column 3.

7. \left[\begin{matrix}1 & 0 & 0 & -24 & 18 & 5\\0 & 1 & 0 & 20 & -15 & -4\\0 & 0 & 1 & -5 & 4 & 1\end{matrix}\right]

   R2 ← R2 − (4)·R3 to clear column 3.

8. A^{-1} = \left[\begin{matrix}-24 & 18 & 5\\20 & -15 & -4\\-5 & 4 & 1\end{matrix}\right]

   Read off the right block.