A = [5,4,1,3],C1 ↔ C2; B = [3,1,4,5],R1 ↔ R2.A = \( \begin{bmatri

1.	A = [5,4,1,3],C1 ↔ C2; B = [3,1,4,5],R1 ↔ R2.A = \( \begin{bmatrix}5& 4 \\[0.3em]1 & 3 \\[0.3em]\end{bmatrix}\),C1 ↔ C2; B = \( \begin{bmatrix}3& 1 \\[0.3em]4 & 5 \\[0.3em]\end{bmatrix}\), R1 ↔ R2.What do you observe?
Answer» Given, A = [5,4,1,3],C₁ ↔ C₂; B = [3,1,4,5],R₁ ↔ R₂. A = \( \begin{bmatrix} 5& 4 \\[0.3em] 1 & 3 \\[0.3em] \end{bmatrix} \) By C₁ ↔ C₂, we get, A ~ \( \begin{bmatrix} 4&5 \\[0.3em] 3 & 1 \\[0.3em] \end{bmatrix} \)....(1) B = \( \begin{bmatrix} 3& 1 \\[0.3em] 4 & 5 \\[0.3em] \end{bmatrix} \) By R₁ ↔ R₂, we get B ~ \( \begin{bmatrix} 4&5 \\[0.3em] 3 & 1 \\[0.3em] \end{bmatrix} \)....(2) From (1) and (2), We observe that the new matrices are equal.

A = [5,4,1,3],C1 ↔ C2; B = [3,1,4,5],R1 ↔ R2.A = \( \begin{bmatrix}5& 4 \\[0.3em]1 & 3 \\[0.3em]\end{bmatrix}\),C1 ↔ C2; B = \( \begin{bmatrix}3& 1 \\[0.3em]4 & 5 \\[0.3em]\end{bmatrix}\), R1 ↔ R2.What do you observe?

Answer»

Given,

A = [5,4,1,3],C₁ ↔ C₂;

B = [3,1,4,5],R₁ ↔ R₂.

A = \( \begin{bmatrix} 5& 4 \\[0.3em] 1 & 3 \\[0.3em] \end{bmatrix} \)

By C₁ ↔ C₂, we get,

A ~ \( \begin{bmatrix} 4&5 \\[0.3em] 3 & 1 \\[0.3em] \end{bmatrix} \)....(1)

B = \( \begin{bmatrix} 3& 1 \\[0.3em] 4 & 5 \\[0.3em] \end{bmatrix} \)

By R₁ ↔ R₂, we get

B ~ \( \begin{bmatrix} 4&5 \\[0.3em] 3 & 1 \\[0.3em] \end{bmatrix} \)....(2)

From (1) and (2),

We observe that the new matrices are equal.

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A = [5,4,1,3],C1 ↔ C2; B = [3,1,4,5],R1 ↔ R2.A = \( \begin{bmatrix}5&amp; 4 \\[0.3em]1 &amp; 3 \\[0.3em]\end{bmatrix}\),C1 ↔ C2; B = \( \begin{bmatrix}3&amp; 1 \\[0.3em]4 &amp; 5 \\[0.3em]\end{bmatrix}\), R1 ↔ R2.What do you observe?

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A = [5,4,1,3],C1 ↔ C2; B = [3,1,4,5],R1 ↔ R2.A = \( \begin{bmatrix}5& 4 \\[0.3em]1 & 3 \\[0.3em]\end{bmatrix}\),C1 ↔ C2; B = \( \begin{bmatrix}3& 1 \\[0.3em]4 & 5 \\[0.3em]\end{bmatrix}\), R1 ↔ R2.What do you observe?