Consider the system of equations \(\left[ {\begin{array}{ccc} 1&3&2\\ 2&2&{ - 3}\\ 4&4&{ - 6}\\ 2&5&2 \end{array}} \right]\left[ {\begin{array}{c} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right] = \left[ {\begin{array}{c} 1\\ 1\\ 2\\ 1 \end{array}} \right]\) The value of x3 (round off to the nearest integer), is ______.
The third equation repeats twice the second. Subtracting twice the first equation from the fourth gives x2+2x3=1. Thus x2=1−2x3 and the first equation gives x1=−2+4x3. Substitute into the second: 2(−2+4x3)+2(1−2x3)−3x3=1, yielding x3=3.
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
