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प्रश्न
If A = `[(2, 1),(0, -2)], B = [(4, 1),(-3, -2)], C = [(-3, 2),(-1, 4)]`, find A2 − 6B + AC.
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उत्तर
A2 = `[(2, 1),(0, -2)] [(2, 1),(0, -2)]`
= `[(2 xx 2 + 1 xx 0, 2 xx 1 + 1 xx (-2)),(0 xx 2 + (-2) xx 0, 0 xx 1 + (-2) xx (-2))]`
= `[(4, 0),(0, 4)]`
6B = `6 xx [(4, 1),(-3, -2)]`
= `[(24, 6),(-18, - 12)]`
AC = `[(2, 1),(0, -2)] xx [(-3, 2),(-1, 4)]`
= `[(2 xx (-3) + 1 xx (-1), 2 xx 2 + 1 xx 4),(0 xx (-3) + (-2) xx (-1), 0 xx 2 + (-2) xx 4)]`
= `[(-6 - 1, 4 + 4),(0 + 2, 0 - 8)]`
= `[(-7, 8),(2, -8)]`
A2 − 6B + AC = `[(4, 0),(0, 4)] - [(24, 6),(-18, - 12)] + [(-7, 8),(2, -8)]`
A2 − 6B = `[(4, 0),(0, 4)] - [(24, 6),(-18, - 12)]`
= `[(4 - 24, 0 - 6),(0 - (-18), 4 - (-12))]`
= `[(-20, -6),(18, 16)]`
A2 − 6B + AC = `[(-20, -6),(18, 16)] + [(-7, 8),(2, -8)]`
= `[(-20 + (-7), -6 + 8),(18 + 2, 16 + (-8))]`
= `[(-27, 2),(20, 8)]`
