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Given Two Matrices a and B `A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]` Find Ab and Use this Result to Solve the Following System of Equations: X - 2y + 3z = 6, X + 4x + Z = 12, - ISC (Commerce) Class 12 - Mathematics

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Question

Given two matrices A and B 

`A = [(1,-2,3),(1,4,1),(1,-3, 2)]  and B  = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`

find AB and use this result to solve the following system of equations:

x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1

Solution

`AB = [(1,-2,3),(1,4,1),(1,-3,2)][(11,-5,-14),(-1,-1,2),(-7,1,6)]`

`AB = [(11+3-21,-5+2+3,-14-4+18),(11-4-7,-5-4+1, -14+8+6),(11+3-14, -5+3+2,-14-6+12)]`

`AB = [(-8,0,0),(0,-8,0),(0,0,-8)] = - 8I`

`-1/8 AB = I`

`A(-1/8 B) = I`

`A^(-1) = -1/8 B`

Let AX= C

`[(1,-2,3),(1,4,1),(1,-3,2)][(x),(y),(z)] = [(6),(12),(1)]`

AX = C

`X= A^(-1)C`

we know that `A^(-1) = (-1)/8 B`

`[(x),(y),(z)] = (-1)/8 [(11,-5,-14),(-1,-1,2),(-7,1,6)] [(6),(12),(1)]`

`[(x),(y),(z)] = (-1)/8[(66,-60,-14),(-6,-12,+2),(-42,+12,+6)]`

`[(x),(y),(z)] =(-1)/8 [(8),(-16),(-24)]`

`[(x),(y),(z)] = [(1),(2),(3)]`

x = 1

y = 2

z = 3

  Is there an error in this question or solution?

APPEARS IN

 2014-2015 (March) (with solutions)
Question 2.2 | 5.00 marks

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Solution Given Two Matrices a and B `A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]` Find Ab and Use this Result to Solve the Following System of Equations: X - 2y + 3z = 6, X + 4x + Z = 12, Concept: Types of Matrices.
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