MtxProperties

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Key points
Look at the following properties that you have noticed so far while doing Addition, Subtraction and Multiplication.


  1. A2x3 + B2x3 = C2x3
    When we Add two matrices of the 'same order' (in this case they are 2x3) it gives another matrix of that same order (in this case a 2x3 matrix.)
  2. A2x3 - B2x3 = C2x3
    When we Subtract two matrices of the 'same order' (in this case they are 2x3) it gives another matrix of that same order (in this case a 2x3 matrix).
  3. Rectangular Matrices;
    • A2x3 × B3x2 = C2x2
      When we Multiply a matrix of order a x b by a matrix of order b x c we get a matrix of order a x c.
    • B3x2 × A2x4 = D3x4
      When we Multiply a matrix of order b x a by a matrix of order a x c we get a matrix of order b x c.

If you look at the above two cases, you will notice that in general
A x B is not equal to B x A.


When do we get a square matrix as the answer?
  • A2x3 × B3x2 = C2x2
    When we Multiply a matrix of order a x b by a matrix of order b x a we get a square matrix of order a x a.
  • A3x3 × B3x3 = C3x3
    When we Multiply a matrix of order a x a by a matrix of order a x a we get a square matrix of order a x a.



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Self Assessment

Check what you have understood so far


Write the order of the matrix that you get as the result of performing the given operation with the two given matrices.(Warning! You might not be able to perform the operation with the given matrices. In that case write "No Answer".

Fill in the blank column.
First matrix Operation Second matrix Resultant matrix
A3x2 + B3x2 C?
A2x3 - B3x2 C?
A3x2 + B2x3 C?
A3x3 - B3x3 C?
A2x3 x B3x3 C?
A3x2 x B2x4 C?
A2x3 x B2x3 C?
A1x3 x B3x1 C?
A2x3 x B2x3 C?
A4x1 x B1x2 C?
A1x2 - B2x3 C?
A3x1 - B1x3 C?


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Multiplication of Matrices

 
(1) I multiplied matrix A by matrix B. The answer was a matrix of order 2 x 3. If the order of A is 2 x 2, what could be the order of B?
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(2) A is a square Matrix. What is the meaning of A2?
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(3) P is a 2 x 3 Matrix. Can you calculate P3?
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You may try the following exercise

Additional Exercises