Question:

The only integral root of the equation $\begin{vmatrix} 2-y &2&3\\ 2 &5-y &6\\ 3 & 4 & 10-y \end{vmatrix}$ =0 is

Updated On: Jul 2, 2022

y = 1
y = 2
y = 3
none of these

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The Correct Option is A

Solution and Explanation

Clearly

y

= 1 satisfies it.

[C_3 = 3C_1]

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Notes on Matrices

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.

The only integral root of the equation ∣2−y2325−y63410−y∣ \begin{vmatrix} 2-y &2&3\\ 2 &5-y &6\\ 3 & 4 & 10-y \end{vmatrix}​2−y23​25−y4​3610−y​​=0 is