Question:
The system of linear equations : $x + y + z = 0, 2x + y - z = 0, 3x + 2y = 0$ has :
The system of linear equations : $x + y + z = 0, 2x + y - z = 0, 3x + 2y = 0$ has :
Updated On: Apr 19, 2024
- no solution
- a unique solution
- an infinitely many solution
- None of these
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The Correct Option is C
Solution and Explanation
The system is homogenuous system.
$\therefore$ it has either unique solution or infinitemany solution depend on $|A|$
$\therefore \left|A\right|=\begin{vmatrix}1&1&1\\ 2&1&-1\\ 3&2&0\end{vmatrix}$
$=2-3+1=0$
$\therefore$ it has either unique solution or infinitemany solution depend on $|A|$
$\therefore \left|A\right|=\begin{vmatrix}1&1&1\\ 2&1&-1\\ 3&2&0\end{vmatrix}$
$=2-3+1=0$
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.