Solve `|[1,-2,3],[5,2,-4],[2,-4,6]|`

Solve: 2X+Y+[[-2,1,3],[5,-7,3],[4,5,4]]=0,X-Y=[[4,7,0],[-1,2,-6],[-2,8,-5]] .

solve for x, if |[3,-5,2],[4,x+1,-1],[2,x-2,3]|=0

Find the rank of matrix : A= [[1,2,-2,3],[2,5,-4,6],[-1,-3,2,-2],[2,4,-1,6]]

Name the octants in which the following points lie: (1,2,3),(4,-2,3),(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1.6),(-2,-4,-7),(-3,1,2),(-3,1,-2)

Solve the matrix equation : ([1,x,1])([1,2,3],[4,5,6],[3,2,5])((1),(2),(3))=(0)

Solve the matrix equation : ([1,x,1])([1,2,3],[4,5,6],[3,2,5])((1),(-2),(3))=(0)

Without expanding prove that: |[12, 2, 4, -5, 1],[-8, 1, -5, 2, -1],[6, 4, a ,-3, 2],[-10, 2, 1 ,3 ,4],[-2, 4, 6 ,8, -5]|=|[12, -4, -8, 10, -2],[4, 1, -5, 2, -1],[-3, 4, a, -3, 2],[5, 2, 1, 3, 4],[1, 4, 6, 8, -5]| .

If A=[[2,3,-4],[1,0,6],[-2,1,5]],B=[[5,1,2],[6,-1,4],[5,3,-4]] , find 2A-3B .

If A=[[2,3,-4],[1,0,6],[-2,1,5]],B=[[5,1,2],[6,-1,4],[5,3,-4]] , find 2A-3B .

Solve: 5x-6=4x-2