Home
Class 12
MATHS
If A=[{:(2,1,2),(1,2,4):}] and B=[{:(4,1...

If `A=[{:(2,1,2),(1,2,4):}]` and `B=[{:(4,1),(2,3),(1,2):}]` Find AB and BA ( if it exist)

Text Solution

AI Generated Solution

To solve the problem of finding the products \( AB \) and \( BA \) for the given matrices \( A \) and \( B \), we will follow these steps: ### Given Matrices: - Matrix \( A = \begin{pmatrix} 2 & 1 & 2 \\ 1 & 2 & 4 \end{pmatrix} \) (2 rows, 3 columns) - Matrix \( B = \begin{pmatrix} 4 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix} \) (3 rows, 2 columns) ### Step 1: Check the dimensions for multiplication To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. ...
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    NCERT EXEMPLAR ENGLISH|Exercise TRUE/FALSE|2 Videos

  • PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise True/False|9 Videos

Similar Questions

Explore conceptually related problems

if A=[{:(4,0,-3),(1,2,0):}]and B=[{:(2,1),(1,-2),(3,4):}]' then find AB and BA.

If A=[{:(,1,4),(,1,-3):}] and B=[{:(,1,2),(,-1,-1):}] , find: (A+B)^2

If A=[{:(,1,2),(,2,1):}] and B=[{:(,2,1),(,1,2):}] find : (i) A(BA) (ii) (AB) B.

Let A=[{:(,1,0),(,2,1):}], B=[{:(,2,3),(,-1,0):}] . Find A^2+AB+B^2

if A=[{:(1,2,3),(4,5,6):}]and B=[{:(-3,-2),(0,1),(-4,-5):}], then find AB and BA ,

If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then AB and BA are defined and equal.

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

If A=[{:(,1),(,2),(,3):}]and B =[{:(,-5,4,0),(,0,2,-1),(,1,-3,2):}]"then AB"

If A=[{:(,-2,3),(,4,1):}] and B=[{:(,1,2),(,3,5):}] , find (i) AB (ii) BA (iii) Is AB=BA? (iv) Write the conclusion that you draw from the result obtained above in (iii).

NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. FindA, if [{:(4),(1),(3):}]A=[{:(-4,8,4),(-1,2,1),(-3,6,3):}]

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |