Question

Select the correct answer from the drop-down menu. HELP.

Answer 1

Answer:

A and D are equal matrices

Step-by-step explanation:

Two matrices are equal if they have the same dimensions (numbers of rows and columns)

∵ $A=-2\left[\begin{array}{cc}-6&4\\3&7\\12&10\end{array}\right]$

- Multiply each element by -2

∴ $A=\left[\begin{array}{cc}12&-8\\-6&-14\\-24&-20\end{array}\right]$

∵ Matrix A has 3 rows and 2 columns

∴ Its dimensions are 3 × 2

∵ Matrix B has 2 rows and 3 columns

∴ Its dimensions are 2 × 3

- Equal matrices has equal dimensions and equal corresponding

   elements

∵ A and B has different dimensions, so they can not be equal

∴ A ≠ B

∵  $3C=3\left[\begin{array}{cc}-2&8\\2&5\\8&6\end{array}\right]$

∴ The dimensions of C are 3 × 2

- Divide the two sides of the matrix by 3 to find C

∴  $C=\left[\begin{array}{cc}-2&8\\2&5\\8&6\end{array}\right]$

∵ A and C have same dimensions but they have different

   corresponding elements

∴ A ≠ C

∵ $D=-1\left[\begin{array}{cc}-12&8\\6&14\\24&20\end{array}\right]$

- Multiply each element by -1

∴  $D=\left[\begin{array}{cc}12&-8\\-6&-14\\-24&-20\end{array}\right]$

∵ The dimensions of D are 3 × 2

∵ The corresponding elements of A and D are equal

∴ A and D are equal matrices