Given a system of equations \(x\; + \;2y\; + \;2z\; = \;{b_1},\;\;\;\;\;5x\; + \;y\; + \;3z\; = \;{b_2}\) Which of the following is true about solutions?
The system will have infinitely many solutions for any given \({b_1}\) and \({b_2}\)
The coefficient matrix has two independent rows, so its map onto the two-dimensional right-hand-side space is surjective. There are three unknowns and rank2, leaving one free parameter. Thus infinitely many solutions for every b1,b2.
Important Questions from System of Linear Equations
Let $A=\begin{bmatrix} 1 & 1 & 1 \\ -1 & -1 & -1 \\ 0 & 1 & -1 \end{bmatrix}$ and $b = \begin{bmatrix} 1/3 \\ -1/3 \\ 0 \end{bmatrix}$, then the system of linear equations $Ax = b$ has
- Let $ \mathbf{A} = \begin{bmatrix} 1 & 1 \\ 1 & 3 \\ -2 & -3 \end{bmatrix} $ and $ \mathbf{b} = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix} $. For $ \mathbf{Ax} = \mathbf{b} $ to be solvable, which one of the following options is the correct condition on $ b_1, b_2 $ and $ b_3 $:
The nine numbers x1, x2, x3 ... x9, are in ascending order. Their average m is strictly greater than all the first eight numbers. Which of the following is true?
For what value of k, the system linear equation has no solution
(3k + 1)x + 3y - 2 = 0
(k2 + 1)x + (k - 2)y - 5 = 0
A system of equations is said to be inconsistent if
