Examine the consistency of the system of equations:
\(x + 2y = 2\)
\(2x + 3y = 3\)
Consistent
Examine the consistency of the system of equations:
\(2x - y = 5\)
\(x + y = 4\)
Consistent
Examine the consistency of the system of equations:
\(x + 3y = 5\)
\(2x + 6y = 8\)
Inconsistent
Examine the consistency of the system of equations:
\(x + y + z = 1\)
\(2x + 3y + 2z = 2\)
\(ax + ay + 2az = 4\)
Consistent
Examine the consistency of the system of equations:
\(3x - y - 2z = 2\)
\(2y - z = -1\)
\(3x - 5y = 3\)
Inconsistent
Examine the consistency of the system of equations:
\(5x - y + 4z = 5\)
\(2x + 3y + 5z = 2\)
\(5x - 2y + 6z = -1\)
Consistent
Solve the system of linear equations, using matrix method:
\(5x + 2y = 4\)
\(7x + 3y = 5\)
\(x = 2,\; y = -3\)
Solve the system of linear equations, using matrix method:
\(2x - y = -2\)
\(3x + 4y = 3\)
\(x = -\frac{5}{11},\; y = \frac{12}{11}\)
Solve the system of linear equations, using matrix method:
\(4x - 3y = 3\)
\(3x - 5y = 7\)
\(x = -\frac{6}{11},\; y = -\frac{19}{11}\)
Solve the system of linear equations, using matrix method:
\(5x + 2y = 3\)
\(3x + 2y = 5\)
\(x = -1,\; y = 4\)
Solve the system of linear equations, using matrix method:
\(2x + y + z = 1\)
\(x - 2y - z = \frac{3}{2}\)
\(3y - 5z = 9\)
\(x = 1,\; y = \frac{1}{2},\; z = -\frac{3}{2}\)
Solve the system of linear equations, using matrix method:
\(x - y + z = 4\)
\(2x + y - 3z = 0\)
\(x + y + z = 2\)
\(x = 2,\; y = -1,\; z = 1\)
Solve the system of linear equations, using matrix method:
\(2x + 3y + 3z = 5\)
\(x - 2y + z = -4\)
\(3x - y - 2z = 3\)
\(x = 1,\; y = 2,\; z = -1\)
Solve the system of linear equations, using matrix method:
\(x - y + 2z = 7\)
\(3x + 4y - 5z = -5\)
\(2x - y + 3z = 12\)
\(x = 2,\; y = 1,\; z = 3\)
If
\[ A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} \]
find \(A^{-1}\). Using \(A^{-1}\) solve the system of equations
\(2x - 3y + 5z = 11\)
\(3x + 2y - 4z = -5\)
\(x + y - 2z = -3\)
\(A^{-1} = \begin{bmatrix} 0 & 1 & -2 \\ -2 & 9 & -23 \\ -1 & 5 & -13 \end{bmatrix}\), \(x = 1,\; y = 2,\; z = 3\)
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is \(\text{₹}60\). The cost of 2 kg onion, 4 kg wheat and 6 kg rice is \(\text{₹}90\). The cost of 6 kg onion 2 kg wheat and 3 kg rice is \(\text{₹}70\). Find cost of each item per kg by matrix method.
Cost of onions per kg = \(\text{₹}5\)
Cost of wheat per kg = \(\text{₹}8\)
Cost of rice per kg = \(\text{₹}8\)