On using elementary row operation R₁→ R₁ – 3R₂ in the following matrix equation:

$[\begin{array}{ll} 4 & 2 \\ 3 & 3 \end{array}] = [\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$ , we have :

Question

Question

On using elementary row operation R₁→ R₁ – 3R₂ in the following matrix equation:

$[\begin{array}{ll} 4 & 2 \\ 3 & 3 \end{array}] = [\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$ , we have :

$[\begin{array}{cc} - 5 & - 7 \\ 3 & 3 \end{array}] = [\begin{array}{cc} 1 & - 7 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$
$[\begin{array}{cc} - 5 & - 7 \\ 3 & 3 \end{array}] = [\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}] [\begin{array}{cc} - 1 & - 3 \\ 1 & 1 \end{array}]$
$[\begin{array}{cc} - 5 & - 7 \\ 3 & 3 \end{array}] = [\begin{array}{cc} 1 & 2 \\ 1 & - 7 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$
$[\begin{array}{cc} 4 & 2 \\ - 5 & - 7 \end{array}] = [\begin{array}{cc} 1 & 2 \\ - 3 & - 3 \end{array}] [\begin{array}{cc} 2 & 0 \\ 1 & 1 \end{array}]$

Answer 1

Explanation:

We have the matrix equation: $[\begin{array}{ll} 4 & 2 \\ 3 & 3 \end{array}] = [\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$

Row operation for the matrix (R1 → R1 – 3R2) we get,

$[\begin{array}{ll} 4 & 2 \\ 3 & 3 \end{array}] = [\begin{array}{ll} - 5 & - 7 \\ 3 & 3 \end{array}]$

⇒ $[\begin{array}{cc} - 5 & - 7 \\ 3 & 3 \end{array}] = [\begin{array}{cc} 1 & - 7 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$ ,

Which is the required answer.

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On using elementary row operation R₁→ R₁ – 3R₂ in the following matrix equation:

$[\begin{array}{ll} 4 & 2 \\ 3 & 3 \end{array}] = [\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$ , we have :

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On using elementary row operation R1 → R1 – 3R2 in the following matrix equation: [4233]=[1203][2011], we have :

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On using elementary row operation R₁→ R₁ – 3R₂ in the following matrix equation:

$[\begin{array}{ll} 4 & 2 \\ 3 & 3 \end{array}] = [\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}] [\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}]$ , we have :