GATE 2020 CE (CE1) – Question 50
For $$\begin{bmatrix}1&3&2\\2&2&-3\\4&4&-6\\2&5&2\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}1\\1\\2\\1\end{bmatrix},$$ find $x_3$, nearest integer.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 3 to 3
Explanation
Subtract twice row 1 from row 4: $-x_2-2x_3=-1$, hence $x_2=1-2x_3$. Row 1 then gives $x_1=-2+4x_3$. Substitute into row 2 to obtain $x_3=3$. The solution $(10,-5,3)$ also satisfies redundant row 3. **3**.