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प्रश्न
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
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उत्तर
X = `[(a, b),(c, d)]`
X`[(1, 2, 3),(4, 5, 6)] = [(a, b),(c, d)][(1, 2, 3),(4, 5, 6)]`
= `[(a + 4b, 2a + 5b, 3a + 6b),(c + 4d, 2c + 5d, 3c + 6d)]`
= `[(-7, -8, -9),(2, 4, 6)]` ...(Given)
Keeping corresponding elements same,
a + 4b = –7 ...(1)
2a + 5b = –8 ...(2)
– – +
3a + 6b = –9 ...(3)
Multiplying equation (1) by 2 and subtracting it from equation (2),
2a + 8b = –14
2a + 5b = –8
– – +
3b = –6
b = –2
Putting the value of b in equation (3),
3a + 6 × (–2) = –9
3a – 12 = –9
3a = 12 – 9
3a = 3
a = 1
Keeping the corresponding elements of the second row same,
c + 4d = 2 ...(4)
2c + 5d = 4 ...(5)
3c + 6d = 6 ...(6)
On multiplying equation (4) by 2 and subtracting it from equation (5), we get
2c + 8d = 4
2c + 5d = 4
– – +
3d = 0
d = 0
Putting the value of d in equation (6),
3c = 6
c = 2
Hence, X = `[(1, -2), (2, 0)]`.
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