Question

Does the following system of equations possess a non – zero solution?
x + 2y + 3z = 0, 3x + 4y + 4z = 0, 7x + 10y + 11z =0
please answer
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Answer 1

Step-by-step explanation:

Write all equations such that in each equation, the order of variables is same, and all the constants are on other side of equality. Eg- in your case, if first equation is written as “first X then Y then Z ”, then all other equations should also be in same order.

Simply put the coefficients of X,Y,Z in a matrix (lets say A )in the order in which they occur (if variable is missing, then coefficient is 0 ), ie, if your equations are as in the problem, then the corresponding matrix will have-

1st row 1 2 3

2nd row 3 4 4

3rd row 7 10 12

Also make a matrix of constants which are on other side of the equality (lets say B ).

3. Find if matrix A is invertible or not. If it is invertible, it has a solution. Find its inverse.

4. Multiply this inverse matrix by matrix B (put inverse of A on left and B on right). You will get a matrix containing same number of elements as there are number of variables in the equation.

Then, your answer is the order in which you have written the variables ie, if you get final matrix like this [4 1 −5] , then your solution would be x=4,y=1,z=−5