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The Class 12 RD Sharma chapter 7 exercise FBQ solution tops all the NCERT solutions as per the opinion of students as well as teachers. Since every CBSE school requires their students to practise and master their NCERT maths book, they are required to answer all the questions that are important for their exam. The RD Sharma class 12th exercise FBQ is said to be quite an efficient guide for the students to help them score high in exams and ace the maths paper.
Also Read - RD Sharma Solution for Class 9 to 12 Maths
Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 1
Answer $\rightarrow a=-1$We know that for infinitely many solution $D=0$
$\Rightarrow\left|\begin{array}{lll} 1 & a & 0 \\ 0 & 1 & a \\ a & 0 & 1 \end{array}\right|=0$
Expanding along row $1$ we get
$\begin{aligned} &\Rightarrow 1(1-0)-a\left(0-a^{2}\right)+0(0-a)=0 \\ &\Rightarrow 1+a^{3}=0 \end{aligned}$
$\begin{aligned} &\Rightarrow a^{3}+1=0 \\ &\Rightarrow a^{3}=-1 \\ &\Rightarrow a=-1 \end{aligned}$
This is required value of $a$
Solution of Simultaneous Linear Exercise Fill in the blank Question 2
Answer $\rightarrow \lambda =3$Solution of Simultaneous Linear Exercise Fill in the blank Question 3
Answer$\rightarrow$ No solution.$\Rightarrow A=\left|\begin{array}{lll} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 5 & 2 \end{array}\right|$
$\begin{aligned} &\Rightarrow|A|=1(6-5)-2(4-3)+1(10-9) \\ &\Rightarrow 1-2+1=0 \\ &\Rightarrow|A|=0 \end{aligned}$
Again we have to find $(a d j A) B$ where $B=\left[\begin{array}{l} 3 \\ 3 \\ 1 \end{array}\right], A=\left[\begin{array}{lll} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 5 & 2 \end{array}\right]$
For $a d j \: A$
$\text { Here, } A=\left[\begin{array}{lll} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 5 & 2 \end{array}\right]$
The cofactor of the elements of $\left | A \right |$ are given by
$A_{11}=\left|\begin{array}{ll} 3 & 1 \\ 5 & 2 \end{array}\right|=1 \quad \quad A_{12}=-\left|\begin{array}{ll} 2 & 1 \\ 3 & 2 \end{array}\right|-1$
$\begin{aligned} &A_{13}=\left|\begin{array}{ll} 2 & 3 \\ 3 & 5 \end{array}\right|=1 \quad \quad A_{21}=-\left|\begin{array}{ll} 2 & 1 \\ 5 & 2 \end{array}\right|=1 \\\\ &A_{22}=\left|\begin{array}{ll} 1 & 1 \\ 3 & 2 \end{array}\right|=-1 \quad \quad A_{23}=-\left|\begin{array}{ll} 1 & 2 \\ 3 & 5 \end{array}\right|=1 \end{aligned}$
$A_{31}=\left|\begin{array}{ll} 2 & 1 \\ 3 & 1 \end{array}\right|=-1 \quad A_{32}=-\left|\begin{array}{ll} 1 & 1 \\ 2 & 1 \end{array}\right|=1$
$A_{33}=\left|\begin{array}{ll} 1 & 2 \\ 2 & 3 \end{array}\right|=-1$
$\text { Then } a d j A=\left[\begin{array}{ccc} 1 & -1 & 1 \\ 1 & -1 & 1 \\ -1 & 1 & -1 \end{array}\right]^{T}$
$\Rightarrow\left[\begin{array}{ccc} 1 & 1 & -1 \\ -1 & -1 & 1 \\ 1 & 1 & -1 \end{array}\right]$
$\text { Then }(a d j A) B=\left[\begin{array}{ccc} 1 & 1 & -1 \\ -1 & -1 & 1 \\ 1 & 1 & -1 \end{array}\right]\left[\begin{array}{l} 3 \\ 3 \\ 1 \end{array}\right]$
$\Rightarrow\left[\begin{array}{c} 3+3-1 \\ -3-3+1 \\ 3+3-1 \end{array}\right]=\left[\begin{array}{c} 5 \\ -5 \\ 5 \end{array}\right] \neq 0$
Here, $(a d j A) B\neq 0$
Hence, the system of equation has no solution.
Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 4
Answer$\rightarrow \lambda=-\frac{5}{3}$Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 5
Answer$\rightarrow k=\pm 1$Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 6
Answer $\rightarrow$Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 7
Answer $\rightarrow$ $k \neq 0, k=\pm 1, \pm 2, \pm 3, \pm 4, \ldots \ldots . \pm n$
Given $\rightarrow$ Given that the system of equations $x+y+z=2,2 x+y-z=3 \text { and } 3 x+2 y+k z=4$ has a unique solution.
To find $\rightarrow$ We have to find the real value of $k$
Hint $\rightarrow$ If the system of equations has a unique solution $\Rightarrow|A| \neq 0$
Solution $\rightarrow$ We have system of equation,
$\begin{aligned} &x+y+z=2 \\ &2 x+y-z=3 \\ &3 x+2 y+k z=4 \end{aligned}$
Then,
$\Rightarrow A=\left[\begin{array}{ccc} 1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k \end{array}\right]$
We know that the system of equations has a unique solution.
$\Rightarrow \left | A \right |$ should not be zero
$\text { i.e. }|A| \neq 0$
$\Rightarrow\left|\begin{array}{ccc} 1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k \end{array}\right| \neq 0$
$\begin{aligned} &\Rightarrow 1(k+2)-1(2 k+3)+1(4-3) \neq 0 \\ &\Rightarrow k+2-2 k-3+1 \neq 0 \\ &\Rightarrow-k \neq 0 \\ &\Rightarrow k=\pm 1, \pm 2, \ldots \ldots \pm n \end{aligned}$
The RD Sharma class 12 solution of Simultaneous linear equation exercise FBQ is highly trusted and recommended by students and teachers across the entire country. The answers provided in the RD Sharma class 12th exercise FBQ are completely handpicked and created by experts, which makes them accurate and understandable enough for students. The experts not only provide answer keys but also some really exceptional tips in the book that the students might not find anywhere else.
The RD Sharma class 12th exercise FBQ solution includes the questions from simultaneous linear equations, where students need to find out the system of equations using real numbers. This exercise FBQ has only 7 questions having a system of equations related to a unique solution, no solution, and infinitely many solutions makes it short and concise to solve. The FBQ section is specifically very essential as it covers the entire chapter’s concept.
The following reasons tells us why the RD Sharma class 12 solutions chapter 7 exercise FBQ is the best guide for students:-
Most importantly the RD Sharma class 12th exercise FBQ is widely trusted by thousands of students in the country.
Solutions are completely prepared by experts which makes it more efficient for practising.
A student might find that most of the questions asked in the board exams are common from the questions in the RD Sharma class 12 chapter 7 exercise FBQ.
RD Sharma class 12th exercise FBQ solution has the latest updated version which is created to correspond with the NCERT textbooks.
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Yes, students can definitely use RD Sharma class 12 chapter 7 ex FBQ for JEE Mains preparation.
Yes, as the RD Sharma class 12th exercise FBQ solution is updated on a regular basis. You can download the latest version from Career360 website.
Of course it can be used for solving homework, as most of the teachers assign work from the same book.
You can self-practice the questions from the NCERT textbooks and the solution from the class 12 RD Sharma chapter 7 exercise FBQ solution to mark yourself.
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