If A=2-3 53 2-41 1-2, find A 1 and hence solve the system of - Maths -

Question

If A = 2 - 3       5 3       2 - 4 1
      1 - 2 , find A −1
and hence solve the system of linear equations
2x − 3y + 5z = 11, 3x +
2y − 4z = −5, x + y
+ 2z = −3

Global Expert · Accepted Answer

Here,A=2-3532-411-2 A =2-3532-411-2     =2-4+4+3-6+4+5(3-2)     =0-6+5     =-1Let Cij be the co factors of the elements aij in Aaij
 Then,C11=-11+12-41-2 =0,                     C12=-11+23-41-2  =2,                C13=-11+33211=1C21=-12+1-351-2  =-1,               C22=-12+2 251-2  =-9,                  C23=-12+32-311=-5C31=-13+1-352-4 =2 ,                  C32=-13+2253-4   =23,                C33=-13+32-332=13adj A=021-1-9-522313T         = 0-122-9231-513⇒A-1=1Aadj A=1-10-122-9231-513The given system of equations can be written in matrix form as follows:2-3532-411-2xyz=11-5-3X=A-1B⇒xyz=1-10-122-9231-51311-5-3⇒xyz=1-10+5-622+45-6911+25-39⇒xyz=1-1-1-2-3⇒ x=-1-1, y=-2-1 and z=-3-1∴ x= 1, y=2 and z= 3

If A = 2 - 3 5 3 2 - 4 1 1 - 2 , find A −1 and hence solve the system of linear equations 2x − 3y + 5z = 11, 3x + 2y − 4z = −5, x + y + 2z = −3

If $A = [\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}]$ , find A ⁻¹ and hence solve the system of linear equations
2x − 3y + 5z = 11, 3x + 2y − 4z = −5, x + y + 2z = −3