Q44 of 44 Page 4

Determine the product [ ccc -4&4&4 -7&1&3 5&-3&-1 ] [ ccc 1&-1&1 1&-2&-2 2&1&3 ] and use it to solve the system of equations x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1.(CBSE 2017)



= 8I3


Now,


we have-


x - y + z = 4


x - 2y - 2z = 9


2x + y + 3z = 1


Writing these equations in matrix form-



⇒ AX = B


where,



If |A| ≠ 0


Then the solution of the equations by matrix method is given by-


X = A-1B


Now,


Expanding along C1


|A| = [(1)(-6+2)-(1)(-3-1)+(2)(2+2)] = [(1)(-4)-(1)(-4)+(2)(4)]


= [-4+4+8]


= 8


we know that-


A(adj A) = |A|In = (adj A)A


Comparing this with



we get-



.


Thus,


.


Hence,


x = 3, y = -2, z = -1

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