find the product of matrices A=[ -5 1 3 7 1 -5 1 -1 1 ], B=[1 1 2 3 - Maths - Matrices

Question

find the product of matrices A=[ -5 1 3 7 1 -5 1 -1 1 ], B=[1 1
2 3 2 1 2 1 3] and use it for solving the equations: x+y+2z=1;
3x+2y+z=7; 2x+y+3z=2

Priyanka Kedia · Accepted Answer

Given, A=-51371-51-11 and B=112321213So,AB=-51371-51-11112321213      =-5+3+6-5+2+3-10+1+97+3-107+2-514+1-151-3+21-2+12-1+3      =400040004      =4100010001      =4I⇒AB=4IPost multiply by B-1 on both side,ABB-1 =4IB-1 ⇒A=4B-1 ⇒B-1 =14A                       
1
Now, given equation be as,x+y+2z=13x+2y+z=72x+y+3z=2Thus, write given system of equation in matrix form,112321213xyz=172This is in the form of BX=C⇒X=B-1C⇒X=14AC                     from equation 1⇒X=14-51371-51-11172         =14-5+7+67+7-101-7+2        =1484-4        =21-1Thus, x=2, y=1 and z=-1

find the product of matrices A=[ -5 1 3 7 1 -5 1 -1 1 ], B=[1 1 2 3 2 1 2 1 3] and use it for solving the equations: x+y+2z=1; 3x+2y+z=7; 2x+y+3z=2.