find rank of Matix\[A=\left[\begin{array}{rrrr}2 & 3 & -1 & -1 \\1 & -

1.	find rank of Matix\[A=\left[\begin{array}{rrrr}2 & 3 & -1 & -1 \\1 & -1 & -2 & -4 \\3 & 1 & 3 & -2\end{array}\right]\]
Answer» \(A=\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\end{bmatrix}\) \(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&4&9&10\end{bmatrix}\) (Applying R₃ → R₃ - R₂& R₂ → 2R₂ - R₁) \(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&0&33&22\end{bmatrix}\) (Applying R₃→ 5R₃ + 4R₂) ∴ Rank of given matrix is 3.

find rank of Matix\[A=\left[\begin{array}{rrrr}2 & 3 & -1 & -1 \\1 & -1 & -2 & -4 \\3 & 1 & 3 & -2\end{array}\right]\]

Answer»

\(A=\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\end{bmatrix}\)

\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&4&9&10\end{bmatrix}\) (Applying R₃ → R₃ - R₂& R₂ → 2R₂ - R₁)

\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&0&33&22\end{bmatrix}\) (Applying R₃→ 5R₃ + 4R₂)

∴ Rank of given matrix is 3.

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find rank of Matix\[A=\left[\begin{array}{rrrr}2 & 3 & -1 & -1 \\1 & -1 & -2 & -4 \\3 & 1 & 3 & -2\end{array}\right]\]

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