Question:
Consider the system of linear equations $ x_1+2x_2+x_3=3\\[0.3em]
2x_1+3x_2+x_3=3 \\[0.3em]3x_1+5x_2+2x_3=1
$ The system has
Consider the system of linear equations $ x_1+2x_2+x_3=3\\[0.3em]
2x_1+3x_2+x_3=3 \\[0.3em]3x_1+5x_2+2x_3=1
$ The system has
Updated On: Jul 6, 2022
- a unique solution
- no solution
- infinite number of solutions
- exactly 3 solutions.
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The Correct Option is B
Solution and Explanation
Adding the first two equations and subtracting the third from the sum, we get $(x_1 + 2x_2 + x_3) + (2x_1 + 3x_2 + x_3) - (3x_1+ 5x_2 + 2x_3)$ = 3 + 1-1
Thus, the system of equation has no solution.
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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.