Determine the product [-4 4 4][1 -1 1] and use it to solve the system of - Maths - Matrices

Question

Determine the product [-4 4 4][1 -1 1] and use it to solve the
system of equations x-y+z=4, x-2y-2z=9, 2x+y+3z=1
[-7 1 3][1 -2 -2]
[5 -3 -1][2 1 3]

Lovina Kansal · Accepted Answer

Dear student
Let A=1-111-2-2213 and C=-444-7135-3-1Then the given product isCA=-444-7135-3-11-111-2-2213CA=-4+4+84-8+4-4-8+12-7+1+67-2+3-7-2+95-3-2-5+6-15+6-3CA=800080008CA=8I318CA=I318CA=I3A-1=18C=18-444-7135-3-1The given system of equations can be written in matrix form as1-111-2-2213 xyz=491Or AX=B wheer A=1-111-2-2213 ,X=xyz and B=491The solution of this system of equations is given byX=A-1BX=18-444-7135-3-1491=18-16+36+4-28+9+320-27-1=1824-16-8=3-2-1So, x=3,y=-2 and z=-1
Regards

Determine the product [-4 4 4][1 -1 1] and use it to solve the system of equations x-y+z=4, x-2y-2z=9, 2x+y+3z=1 [-7 1 3][1 -2 -2] [5 -3 -1][2 1 3]

Determine the product [-4 4 4][1 -1 1] and use it to solve the system of equations x-y+z=4, x-2y-2z=9, 2x+y+3z=1

[-7 1 3][1 -2 -2]
[5 -3 -1][2 1 3]