Mashaal Masha

Question:

 

Which of the following matrices are equal?

 

A = $\left[ 3 \right]$

B =$~\left[ \begin{matrix} 3 & 5 \\ \end{matrix} \right]$

C = $\left[ 5-2 \right]$

D = $\left[ \begin{matrix} 5 & 3 \\ \end{matrix} \right]$
E = $~\left[ \begin{matrix} 4 & 0 \\ 6 & 2 \\ \end{matrix} \right]$ F = $\left[ \begin{matrix} 2 \\ 6 \\ \end{matrix} \right]$
G = $\left[ \begin{matrix} 3-1 \\ 3+3 \\ \end{matrix} \right]$ H = $\left[ \begin{matrix} 4 & 0 \\ 6 & 2 \\ \end{matrix} \right]$
I = $\left[ \begin{matrix} 3 & 3+2 \\ \end{matrix} \right]$ J = $\left[ \begin{matrix} 2+2 & 2-2 \\ 2+4 & 2+0 \\ \end{matrix} \right]$

 

Difficulty: Easy

Solution:

Solving C

C = $\left[ 5-2 \right]$

C = $\left[ 3 \right]$

 

Solving G

G = $\left[ \begin{matrix} 3-1 \\ 3+3 \\ \end{matrix} \right]$

G = $\left[ \begin{matrix} 2 \\ 6 \\ \end{matrix} \right]$

 

Solving I

I = $\left[ \begin{matrix} 3 & 3+2 \\ \end{matrix} \right]$

I = $\left[ \begin{matrix} 3 & 5 \\ \end{matrix} \right]$

 

Solving J

J = $\left[ \begin{matrix} 2+2 & 2-2 \\ 2+4 & 2+0 \\ \end{matrix} \right]$

J = $\left[ \begin{matrix} 4 & 0 \\ 6 & 2 \\ \end{matrix} \right]$

 

Now Matrices are said to be equal if

(i) They are of same order

(ii) Their corresponding values are equal

 

So, according to this definition

(a) Matrices A and C are equal, A = C.

(b) Matrices B and I are equal, B = I.

(c) Matrices E, H and J are equal, E = H = J.

(d) Matrices F and G are equal, F = G.

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