If A, B and C are three matrices of order 2 × 3, 3 × 2 and 3 × 3, then the matrices given in which of the following options are defined?

  • A)

    A + B, A + BT, (AB) T

  • B)

    (AB) T, ACBT, A B

  • Next
  • clear
"C)

ACBT, AC + BT, AB

  • Next
  • clear
  • "D)

    4C, ACBT, CTB + A

    the order of the matrix A is 2*3
    the order of matrix B is 3*2
    the order of matrix C is 3*3
    since the order of the matrix A and B are not same.
    therefore A+B is not defined.
    thus option (a) is wrong
    the number of columns in matrix A is equal to the number of rows in matrix B.
    thus AB is defined and transpose of AB is also defined.
    the number of columns in matrix A is equal to the number of rows in matrix C.
    thus AC is defined ad order of AC is 2*3
    the order of transpose of B is 2*3.
    since the number of columns in matrix AC is not equal to number of rows in  transpose of matrix B.
    thus ACBT is not defined and option (b) is wrong

    from the above ACBT is not defined thus option (c) is wrong.

    the order of AC and BT is same . thus the sum is defined. thus AC+BT is defined.

    hope this helps you


     

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