A matrix X has a + b rows and a + 2 columns while the matrix Y ha… - Vidyadip

Question

A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say XY and YX are of the same type? Are they equal.

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Answer

Here,

[X]_{(a+b) × (a+2)}

[Y]_{(b+1) × (a+3)}

Since XY exists, the number of columns in X is equal to the number of rows in Y.

⇒ a + 2 = b + 1 ...(1)

Similarly, since YX exists, the number of columns in Y is equal to the number of rows in X.

⇒ a + b = a + 3

⇒ b = 3

Putting the value of b in (1), we get

a + 2 ≈ 3 + 1

⇒ a = 2

Since the order of the matrices XY and YX is not same, XY and YX are not of the same type and they are unequal.

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