Which of the following matrices can NOT be obtained from the matrix <math><mrow><mrow><mo>[</mo><mrow><mtable><mtr columnalign="center"><mtd columnalign="center"><mo>−</mo><mn>1</mn></mtd><mtd columnalign="center"><mn>2</mn></mtd></mtr><mtr columnalign="center"><mtd columnalign="center"><mn>1</mn></mtd><mtd columnalign="center"><mo>−</mo><mn>1</mn></mtd></mtr></mtable></mrow><mo>]</mo></mrow></mrow></math> by a single elementary row operation?

A=[−121−1] EA=[acbd][−121−1]=[−a+c2a−c−b+d2b−d]For a = c For −a+c=02a−c=1]→a=1,c=1 E=[1101]d = b + 1, d = 1, b = 0b+d=12b−d=−1]→b=0,d=1 R1→R1→R2[1001]For −a+c=12a−c=1]→a=0,c=1For−a+c=−12a−c=2]→a=1,c=0−b+d=−22b−d=7]→b=5,d=3 [1053] [1001]R2 → 5R1 + 3R2For For−a+c=−12a−c=2]→a=1,c=1−b+d=−12b−d=3]→b=2,d=1(A) R1 → R1 + R2(B) R2 → R2 + 2R1 [1021] [1001](C) R2 → 3R2 + 5R1

Which of the following matrices can NOT be obtained from the matrix&nbsp;<math><mrow><mrow><mo>[</mo><mrow><mtable><mtr columnalign="center"><mtd columnalign="center"><mo>−</mo><mn>1</mn></mtd><mtd columnalign="center"><mn>2</mn></mtd></mtr><mtr columnalign="center"><mtd columnalign="center"><mn>1</mn></mtd><mtd columnalign="center"><mo>−</mo><mn>1</mn></mtd></mtr></mtable></mrow><mo>]</mo></mrow></mrow></math>&nbsp;by a single elementary row operation?

Ask & Answer Question

Maths Class 12th Maths Matrices

Which of the following matrices can NOT be obtained from the matrix $[\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]$ by a single elementary row operation?

Option 1 -

$[\begin{matrix} 0 & 1 \\ 1 & - 1 \end{matrix}]$

Option 2 -

$[\begin{matrix} 1 & - 1 \\ - 1 & 2 \end{matrix}]$

Option 3 -

$[\begin{matrix} - 1 & 2 \\ - 2 & 7 \end{matrix}]$

Option 4 -

$[\begin{matrix} - 1 & 2 \\ - 1 & 3 \end{matrix}]$

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

$A = [\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]$ $E A = [\begin{matrix} a & c \\ b & d \end{matrix}] [\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]$

$= [\begin{matrix} - a + c & 2 a - c \\ - b + d & 2 b - d \end{matrix}]$

For a = c For $\begin{matrix} - a + c = 0 & 2 a - c = 1 \end{matrix}] \to a = 1, c = 1 E = [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}]$

d = b + 1, d = 1, b = 0

$\begin{matrix} b + d = 1 & 2 b - d = - 1 \end{matrix}] \to b = 0, d = 1 R_{1} \to R_{1} \to R_{2} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

For $\begin{matrix} - a + c = 1 & 2 a - c = 1 \end{matrix}] \to a = 0, c = 1$

$F o r \begin{matrix} - a + c = - 1 & 2 a - c = 2 \end{matrix}] \to a = 1, c = 0$

$\begin{matrix} - b + d = - 2 & 2 b - d = 7 \end{matrix}] \to b = 5, d = 3 [\begin{matrix} 1 & 0 \\ 5 & 3 \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

R₂ → 5R₁ + 3R₂

For $F o r \begin{matrix} - a + c = - 1 & 2 a - c = 2 \end{matrix}] \to a = 1, c = 1$

$\begin{matrix} - b + d = - 1 & 2 b - d = 3 \end{matrix}] \to b = 2, d = 1$

(A) R₁ → R₁ + R₂

(B) R₂→ R₂ + 2R₁ $[\begin{matrix} 1 & 0 \\ 2 & 1 \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
687k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Which of the following matrices can NOT be obtained from the matrix $[\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]$ by a single elementary row operation?

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

Which of the following matrices can NOT be obtained from the matrix [−121−1] by a single elementary row operation?

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

Which of the following matrices can NOT be obtained from the matrix $[\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]$ by a single elementary row operation?