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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Find x, y, z if {3[200222]-4[11-1231]}[12] = [x-3y-12z]

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प्रश्न

Find x, y, z if `{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)]` = `[("x" - 3),("y" - 1),(2"z")]`

बेरीज
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उत्तर

`{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)] = [("x" - 3),("y" - 1),(2"z")]`

∴ `{[(6, 0),(0, 6),(6, 6)] - [(4, 4),(-4, 8),(12, 4)]} [(1),(2)] = [("x" - 3),("y" - 1), (2"z")]`

∴ `[(6 - 4, 0-4),(0+4, 6-8),(6-12, 6-4)] [(1),(2)] = [("x" - 3),("y" - 1), (2"z")]`

∴ `[(2, -4),(4, -2),(-6, 2)] [(1),(2)] = [("x" - 3),("y" - 1), (2"z")]`

∴ `[(2 - 8),(4 - 4),(-6 + 4)] = [("x" - 3),("y" - 1),(2"z")]`

∴ `[(-6),(0),(-2)] = [("x" - 3),("y" - 1),(2"z")]`

∴ by equality of matrices,

x – 3 = –6, y – 1 = 0, 2z = – 2

∴ x = – 3, y = 1, z = –1.

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पाठ 4: Determinants and Matrices - Exercise 4.6 [पृष्ठ ९५]

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