Download App

Solution of Simultaneous Linear Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsSolution of Simultaneous Linear Equations2 Marks
Question
If $\begin{bmatrix}1&0&0\\0&\text{y}&0\\0&0&1\end{bmatrix}\begin{bmatrix}\text{x}\\-1\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$, find x, y and z.
✓

Answer

Here,
$\begin{bmatrix}1&0&0\\0&\text{y}&0\\0&0&1\end{bmatrix}\begin{bmatrix}\text{x}\\-1\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$
$\Rightarrow\begin{bmatrix}\text{x}\\-\text{y}\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$
$\therefore\ \text{x}=1,\text{y}=0\text{ and }\text{z}=1$

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 "2 Marks" from Solution of Simultaneous Linear Equations→Solution of Simultaneous Linear Equations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, find the angle between $\vec{\text{a}}+\vec{\text{b}}$ and $\vec{\text{a}}-\vec{\text{b}}.$
→
Consider f: {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f–1 and show that (f–1)–1 = f.
→
For given vectors, $\vec a = 2\hat i - \hat j + 2\hat k$ and $\vec b = - \hat i + \hat j - \hat k$, find the unit vector in the direction of the vector $\vec a + \vec b$.
→
The following defines a relation on N:
xy is square of an integer, $\text{x, y}\in\text{N}$
Determine which of the above relations are reflexive, symmetric and transitive.
→
Find X and Y, if $2 \mathrm{X}+3 \mathrm{Y}=\left[\begin{array}{ll} {2} & {3} \\ {4} & {0} \end{array}\right] \text { and } 3 \mathrm{X}+2 \mathrm{Y}=\left[\begin{array}{cc} {2} & {-2} \\ {-1} & {5} \end{array}\right]$
→
For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if 
$\vec{\text{a}}=\lambda\hat{\text{i}}+3\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$
→
Find which of the binary operations are commutative and which are associative.
State whether the following statements are true or false. Justify
If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a
→
If $|\vec{\text{a}}|=10,\big|\vec{\text{b}}\big|=2$ and $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=16,$ find $\vec{\text{a}}.\vec{\text{b}}.$
→
Write minors and cofactors of the elements of $\left|\begin{array}{cc}2 & -4 \\ 0 & 3\end{array}\right|$.
→
Evaluate the following integrals:
$\int\cot^{-1}\Big(\frac{\sin2\text{x}}{1-\cos2\text{x}}\Big)\text{dx}$
→