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Give an example of two non-zero 2xx2 ...

Give an example of two non-zero `2xx2` matrices `A` and `B` such that `A B=O` .

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To find two non-zero \(2 \times 2\) matrices \(A\) and \(B\) such that \(AB = O\) (where \(O\) is the zero matrix), we can follow these steps: ### Step 1: Define the Matrices Let's define the matrices \(A\) and \(B\) as follows: \[ A = \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 0 \\ 1 & 2 \end{pmatrix} \] ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. If A[{:(3,-4),(1,1),(2,0):}] and B=[{:(2,1,2),(1,2,4):}] and B=[{:(4,1...

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  2. If A=[{:(2,1,2),(1,2,4):}] and B=[{:(4,1),(2,3),(1,2):}] Find AB and B...

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  3. Give an example of two non-zero 2xx2 matrices A and B such that A B...

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  4. Given A=[{:(2,4,0),(3,9,6):}] "and" B=[{:(1,4),(2,8),(1,3):}], is (AB)...

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  5. Solve for x and y , x[{:(2),(1):}]+y[{:(3),(5):}]+[{:(-8),(-11):}]=0.

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  6. If X and Y are 2xx2 matrices, then solve the following matrix equat...

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  7. If A=[3 5],B=[7 3], then find a non-zero matrix C such that AC=BC.

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  8. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

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  9. If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}] and C=[{:(1,0),(-1,0):}],...

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  10. If P=[x0 0 0y0 0 0z] and Q=[a0 0 0b0 0 0c] , prove that P Q=[x a0 0 0y...

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  11. If [2 1 3] [{:(-1,0,-1),(-1,1,0),(0,1,1):}][{:(1),(0),(-1):}]=A, then ...

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  12. If A=[{:(2, 1,),(4,2,)],B =[{:(2,3,4),(1,4,0):}] and C=[{:(-1,2,1),(1,...

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  13. If A=[{:(1,0,-1),(2,1,3),(0,1, 1):}] then verify that A^(2)+A=A(A+I) ,...

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  14. If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify...

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  15. If A=[{:(1,2),(4,1),(5,6):}] and B=[{:(1,2),(6,4),(7,3):}], then varif...

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  16. Show that A' A and A A' are both symmetric matrices for any matrix A.

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  17. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

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  18. Show that , if A and B are square matrices such that AB=BA, then (A+B)...

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  19. If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}] a=4 an...

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  20. If A=[{:(cos q,sin q),(-sin q, cos q):}] , then variefy that A^(2)=[{:...

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