Show that the following system of linear equations is consistent … - Vidyadip

Question

Show that the following system of linear equations is consistent and also find solutions:x - y + z = 3
2x + y - z = 2
-x - 2y + 2z = 1

✓

Answer

Here,
$\text{x}-\text{y}+\text{z}=3\ \dots(1)$
$2\text{x}+\text{y}-\text{z}=2\ \dots(2)$
$-\text{x}-2\text{y}+2\text{z}=1 \ \dots(3)$
Or, $\text{AX}=\text{B}$
Where,
$\text{A}=\begin{bmatrix}1&-1&1\\ 2&1&-1\\ -1&-2&2\end{bmatrix},\text{X}=\begin{bmatrix}\text{x}\\ \text{y}\\ \text{z}\end{bmatrix}\text{and }\text{B}=\begin{bmatrix}3\\ 2\\ 1\end{bmatrix}$
$\begin{bmatrix}1&-1&1\\ 2&1&-1\\ -1&-2&2\end{bmatrix}\begin{bmatrix}\text{x}\\ \text{y}\\ \text{z}\end{bmatrix}=\begin{bmatrix}3\\ 2\\ 1\end{bmatrix}$
$\text{|A|}=\begin{vmatrix}1&-1&1\\ 2&1&-1\\ -1&-2&2\end{vmatrix}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(5 Marks)" from Solution of Simultaneous Linear Equations→Solution of Simultaneous Linear Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the interest is compounded continuously at $6\%$ per annum, how much worth Rs $100$ will be after $10$ years? How long will it take to double Rs $1000$?

Show that the following system of linear equations is consistent and also find solution:
$2x + 2y − 2z = 1$
$4x + 4y − z = 2$
$6x + 6y + 2z = 3$

Find all point of discontinuity of the function $\text{f(t)}=\frac{1}{\text{t}^2+\text{t}-2},$ where $\text{t}=\frac{1}{\text{x}-1}$

Using differentials, find the approximate values of the following:
$\cos\Big(\frac{11\pi}{36}\Big)$

Evaluate the following integrals:
$\int\frac{\text{x}}{\sqrt{\text{x}^2+\text{a}^2}+\sqrt{\text{x}^2-\text{a}^2}}\text{ dx}$

Differentiate the following w. r. t. x.$(\sin x)^{\tan x}-x^{\log x}$

Compute the adjoint of the following matrices:$\begin{bmatrix}2 & -1 & 3 \\4 & 2 & 5 \\ 0 & 4 & -1 \end{bmatrix}$
Verify that (adj A)A = |A|I = A (adj A) for the above matrices.

The top of a ladder $6$ metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is $4$ metres from the wall, it is sliding away from the wall at the rate of 0.5m/ sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?

Find the coordinates of the foot of the perependicular drawn from the origin to the plane 2x - 3y + 4z - 6 = 0.

Show that the function $\text{f(x)}=\begin{cases}|2\text{x}-3||\text{x}|, & \text{x}\geq1\\\sin\Big(\frac{\pi\text{x}}{2}\Big),& \text{x}>1\end{cases}$ is continuous but not differentiable at x = 1.