Question:

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
Show Solution
collegedunia
Verified By Collegedunia

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).
Was this answer helpful?
0
0

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:

  1. 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.
  2. Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
  3. 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. 
  4. 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. 
  5. Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.