Download App

Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
Question
Find the values of the determinants $:\left|\begin{array}{lll}\mathrm{a} & \mathrm{h} & \mathrm{g} \\ \mathrm{h} & \mathrm{b} & \mathrm{f} \\ \mathrm{g} & \mathrm{f} & \mathrm{c}\end{array}\right|$
✓

Answer

$\left|\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right|=a\left|\begin{array}{ll}b & f \\ f & c\end{array}\right|-h\left|\begin{array}{cc}h & f \\ g & c\end{array}\right|+g\left|\begin{array}{cc}h & b \\ g & f\end{array}\right|$
$ =a\left(b c-f^2\right)-h(h c-g f)+g(h f-g b)$
$ =a b c-a f^2-h^2 c+f g h+f g h-g^2 b$
$ =a b c+2 f g h-a f^2-b g^2-c h^2$
$ =(-15)-(-4)(7)$
$ =-30+28$
$ =-2$

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 "Answer the following questions in short." from Determinants and Matrices→Determinants and Matrices — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $A=\left[\begin{array}{ccc}4 & 3 & 2 \\ -1 & 2 & 0\end{array}\right], B=\left[\begin{array}{cc}1 & 2 \\ -1 & 0 \\ 1 & -2\end{array}\right]$, show that matrix $A B$ is non singular.
→
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{ccc}2 & 0 & 0 \\ 3 & -1 & 0 \\ -7 & 3 & 1\end{array}\right]$

→
If $A=\left[\begin{array}{cc}-3 & 2 \\ 2 & -4\end{array}\right], B=\left[\begin{array}{cc}1 & x \\ y & 0\end{array}\right]$ and $(A+B)(A-B)=A^2-B^2$, find $x$ and $y$.
→
Find the centre and radius of the following circles:
$\left(x-\frac{1}{2}\right)^2+\left(y+\frac{1}{3}\right)^2=\frac{1}{36}$
→
Write each of the following equations in ax + by + c = 0 form :

$\frac{x}{2}+\frac{y}{4}=1$

→
Sunita and Samrudhi who live in Mumbai wish to go on holiday to Delhi together. They can travel to Delhi from Mumbai either by car or by train or plane and on reaching Delhi they can go for city-tour either by bus or Taxi. Describe the sample space, showing all the combined outcomes of different ways they could complete city-tour from Mumbai.
→
$A(1,2), B(2,3)$ and $C(-2,5)$ are vertices of $\triangle \mathrm{ABC}$. Find the slope of the altitude drawn from $\mathrm{A}$.
→
Show that following pairs of lines are perpendicular to each other : $y=2 x+23$ and $2 x+4 y=27$
→
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{lll}9 & \sqrt{2} & -3\end{array}\right]$

→
Evaluate:

$\left|\begin{array}{ccc}2 & -5 & 7 \\ 5 & 2 & 1 \\ 9 & 0 & 2\end{array}\right|$

→