Question:
If the three linear equations $x + 4ay + az = 0$
$x + 3 by + bz = 0$ and
$x + 2cy + cz = 0$ have a non-trivial solution, then a, b, c are in
If the three linear equations $x + 4ay + az = 0$
$x + 3 by + bz = 0$ and
$x + 2cy + cz = 0$ have a non-trivial solution, then a, b, c are in
Updated On: Jul 2, 2022
- A.P
- G.P.
- H.P
- none of these.
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The Correct Option is C
Solution and Explanation
- For non-trival solution $\begin{vmatrix}1&4a&a\\ 1&3b&b\\ 1&2c&c\end{vmatrix}$ = 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.