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The matrix A has x rows and x+5 columns. The matrix B has y rows and 11- y columns. Both AB and BA exist. What are the values of x and y respectively?

Options

  1. A8 and 3
  2. B3 and 4
  3. C3 and 8
  4. D8 and 8

Correct answer

C. 3 and 8

Step-by-step solution

Given, Matrix A has x rows and x+5 columns Matrix B has y rows and 11- y columns. Also given AB and BA exists. If A B exists, then the number of rows in A most be equal to number of columns in B . i.e., x=11-y (1) If BA exists, then the number of rows in B must be equal to number of rows in A . aligned & i.e., x+5=y & 11-y+5=y( from (1)) & 2 y=16 aligned (1) x=11-8=3 . So, x=3, y=8 .

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