Question:
The value of $
\begin{vmatrix}
b+c&a&a\\
b &c+a &b\\
c & c &a+b
\end{vmatrix}$ is
The value of $
\begin{vmatrix}
b+c&a&a\\
b &c+a &b\\
c & c &a+b
\end{vmatrix}$ is
Updated On: Jul 2, 2022
- abc
- (a + b) (b + c) (c + a)
- 4abc
- none of these
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The Correct Option is C
Solution and Explanation
Operate $R_1 - R_2 - R_3$, we get the given det.
$\begin{vmatrix}0 &-2c&-2b\\ b &c+a&b\\ c&c&a+b\end{vmatrix} = 4 abc$ (on simplification).
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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.