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

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

A

identify

B

symmetric matrix

C

skew-symmetric matrix

D

none of these

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To determine the nature of the given matrix \( A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{pmatrix} \), we will analyze it step by step. ### Step 1: Identify the type of matrix The matrix \( A \) is a diagonal matrix because all the non-diagonal elements are zero. **Hint:** A diagonal matrix has non-zero elements only on its main diagonal. ### Step 2: Check if it is an Identity Matrix ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. If A=[{:(0,1),(1,0):}] then A^(2) is equal to

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  2. If matrix A=[a(ij)](2X2), where a(ij)={[1,i!=j],[0,i=j]}, then A^2 i...

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

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  4. The matrix A=[0-5 8 5 0 12-8-12 0] is a (a) diagonal matrix (b) symmet...

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  5. If A is matrix of order mxxn and B is a matrix such that AB' and B'A ...

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  6. if A and B are matrices of same order, then (AB'-BA') is a 1) null mat...

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  7. If A is a square matrix such that A^(2)= I, then (A-I)^(3)+(A+I)^(3)...

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  8. For any two matrices A and B , we have

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  9. On usign elementry column operation C(2)rArrC(2)-2C(1) in the followin...

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  10. On using row operation R(1)rArrR(1)-3R(2) in the following matrix equa...

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  11. ......... Matrix is both symmetric and skew-symmetric matrix.

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  12. Sum of two skew-symmetric matrices is always ......... Matrix.

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  13. The negative of a matrix is obtained b y multiplying it by ...........

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  14. The product of any matrix by the scalar ......... Is the null matrix.

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  15. A matrix which is not a square matrix is called a..........matrix.

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  16. Matrix multiplication is distributive over matrix addition

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  17. If A is a symmetric matrix , then A^(3) is a ........ Matrix.

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  18. If A is a skew-symmetric matrix, then A^(2) is a .................

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  19. If A and B are square matrices of the same order, then (i) (AB)=.......

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  20. If A is a skew-symmetric, then kA is a...........(where, k is any scal...

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