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प्रश्न
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A + B)T = AT + BT = BT + AT
उत्तर
AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`
AT = `[(4, 5),(-1, 0),(2, 3)]`
(AT)T = `[(4, 5),(-1, 0),(2, 3)]^"T"`
A = `[(4, -1, 2),(5, 0, 3)]`
BT = `[(2, 7),(-1, 5),(1, -2)]`
A + B = `[(4, -1, 2),(5, 0, 3)]+ [(2, -1, 1),(7, 5, -2)]`
A + B = `[(4 + 2, -1 - 1, 2 +1),(5 + 7, + 5, 3 -2)]`
= `[(6, -2, 3),(12, 5, 1)]`
(A + B)T = `[(6, 12),(-2, 5),(3, 1)]` .......(1)
AT + BT = `[(4, 5),(-1, 0),(2, 3)] [(2, 7),(-1, 5),(1, -2)]`
= `[(4 + 2, 5 +7),(-1 - 1, 0 + 5),(2 + 1, 3 - 2)]`
(A + B)T = `[(6, 12),(-2, 5),(3, 1)]` .......(2)
BT + AT = `[(2, 7),(-1, 5),(1, -2)] + [(4, 5),(-1, 0),(2, 3)]`
= `[(2 + 4, 7 + 5),(-1 - 1, 5 + 0),(1 + 2, -2 + 3)]`
BT + AT = `[(6, 12),(-2, 5),(3, 1)]` .......(3)
From eqution (1), (2) and (3)
(A + B)T = AT + BT = BT + AT
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