Home
Class 12
MATHS
Matrix [{:(1,0),(0,1):}]is :...

Matrix `[{:(1,0),(0,1):}]`is :

A

Zero matrix

B

Identity matrix

C

Scalar matrix

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To determine the type of the given matrix \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\), we can analyze its properties step by step. ### Step 1: Identify the Matrix The given matrix is: \[ A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \] ### Step 2: Check for Identity Matrix An identity matrix is defined as a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. - In our matrix \(A\), the diagonal elements are \(1\) (first row, first column and second row, second column) and the off-diagonal elements are \(0\) (first row, second column and second row, first column). - Therefore, since it meets the criteria, we conclude that \(A\) is an identity matrix. ### Step 3: Check for Scalar Matrix A scalar matrix is a diagonal matrix in which all the diagonal elements are the same. - In our matrix \(A\), the diagonal elements are both \(1\), which are the same. Therefore, \(A\) is also a scalar matrix. ### Step 4: Conclusion Since the matrix \(A\) is both an identity matrix and a scalar matrix, we can summarize the findings: - The given matrix is an **identity matrix**. - The given matrix is also a **scalar matrix**. ### Final Answer The matrix \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) is an **identity matrix** and also a **scalar matrix**. ---
To determine the type of the given matrix \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\), we can analyze its properties step by step. ### Step 1: Identify the Matrix The given matrix is: \[ A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \] ...
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 3f|10 Videos

  • MATRICES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 3.1|10 Videos

  • MATRICES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 3d|3 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|9 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x_(1), y_(1)) . So, x_(1)=x and y(1)=-y . This may be written as : {(x_(1)=1. x+0.y),(y_(1)=0. x+(-1)y):} This system of equations can be put in the matrix as : [(x_(1)),(y_(1))]=[(1,0),(0,-1)][(x),(y)] Here, matrix [(1,0),(0,-1)] is the matrix of reflection about x-axis. Then find the matrix of reflection about the line y=x .

The identity matrix I_(2)={:[(1,0),(0,1)]:} . If A={:[(2,-3),(5,1)]:} , evaluate AI_(2)=I_(2)A=A

If the matrix {:[(a,b),(c,d)]:} is commutative with matrix {:[(1,1),(0,1)]:} , then

find the transpose of the matrix A=[{:(1,3,-4),(0,2,1):}].

find the transpore of matrix A=[{:(2,0),(-1,4):}].

if the product of n matrices [(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)]…[(1,n),(0,1)] is equal to the matrix [(1,378),(0,1)] the value of n is equal to

Show that A is a symmetric matrix if A= [ (1,0), (0, -1)]

the matrix [(0,1),(1,0)] is the matrix reflection in the line

The matrix [(0,1),(1,0)] is the matrix of reflection in the line (A) x-y=0 (B) x+y=0 (C) x-y=1 (D) x+y=1

The matrix [{:(1,0,0),(0,2,0),(0,0,4):}] is a