Register

ISI 2019 | PCB Mathematics | Question: 14

• edited by
238 views

1 Answer

1 votes
1 votes
Given : $\begin{bmatrix} &1 &2 &1 &-1 \\ &2 &0 &t &0\\ &0 &-4 &5 &2 \end{bmatrix}$

Convert the given matrix to Echelon form.

 Apply $R2\rightarrow R2 - 2R1$        $\begin{bmatrix} &1 &2 &1 &-1 \\ &0 &-4 &t-2 &2\\ &0 &-4 &5 &2 \end{bmatrix}$

Apply $R3\rightarrow R3\ -\ R2$         $\begin{bmatrix} &1 &2 &1 &-1 \\ &0 &-4 &t-2 & 2\\ &0 &0 &7-t &0 \end{bmatrix}$  

It is given that the Rank is 2 which means the number of Linearly Independent Rows(or Columns) is 2 which is the number of pivots.

Here we already have two pivots which are 1 and -4.

$\therefore 7-t\ can't\ be\ a\ pivot$

$\Rightarrow 7-t=0$

$\Rightarrow t=7\ (ans)$
User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 votes
0 votes
1 answer
1
admin asked Aug 8, 2022
357 views
ISI 2019 | PCB Mathematics | Question: 16
Let $\Omega=\{1,2,3, \ldots, 100\}$. In how many ways $ a_{1}<a_{2}<a_{3}<a_{4}<a_{5}, \quad a_{i} \in \Omega $ can be chosen from $\Omega$ such that $a_{i+1}-a_{i} \geq 2$ for each $i?$
Let $\Omega=\{1,2,3, \ldots, 100\}$. In how many ways $$ a_{1}<a_{2}<a_{3}<a_{4}<a_{5}, \quad a_{i} \in \Omega $$ can be chosen from $\Omega$ such that $a_{i+1}-a_{i} \ge...
User Avatar
0 votes
0 votes
1 answer
2
admin asked Aug 8, 2022
100 views
ISI 2019 | PCB Mathematics | Question: 18
Let $N=1 !+2 !+\cdots+2020!.$ Find the remainder obtained when $N$ is divided by $8 .$
Let $N=1 !+2 !+\cdots+2020!.$ Find the remainder obtained when $N$ is divided by $8 .$
User Avatar
0 votes
0 votes
0 answers
4
admin asked Aug 8, 2022
318 views
ISI 2019 | PCB Mathematics | Question: 1
Let $\left\{a_{n}\right\}$ be a decreasing sequence such that $\displaystyle{}\sum_{n=1}^{\infty} a_{n}$ is convergent. Prove that the sequence $\left\{n a_{n}\right\}$ goes to zero as $n \rightarrow \infty$.
Let $\left\{a_{n}\right\}$ be a decreasing sequence such that $\displaystyle{}\sum_{n=1}^{\infty} a_{n}$ is convergent. Prove that the sequence $\left\{n a_{n}\right\}$ g...
User Avatar
Link Copied!