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)
∵ [tex]A=-2\left[\begin{array}{cc}-6&4\\3&7\\12&10\end{array}\right][/tex]
- Multiply each element by -2
∴ [tex]A=\left[\begin{array}{cc}12&-8\\-6&-14\\-24&-20\end{array}\right][/tex]
∵ 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
∵ [tex]3C=3\left[\begin{array}{cc}-2&8\\2&5\\8&6\end{array}\right][/tex]
∴ The dimensions of C are 3 × 2
- Divide the two sides of the matrix by 3 to find C
∴ [tex]C=\left[\begin{array}{cc}-2&8\\2&5\\8&6\end{array}\right][/tex]
∵ A and C have same dimensions but they have different
corresponding elements
∴ A ≠ C
∵ [tex]D=-1\left[\begin{array}{cc}-12&8\\6&14\\24&20\end{array}\right][/tex]
- Multiply each element by -1
∴ [tex]D=\left[\begin{array}{cc}12&-8\\-6&-14\\-24&-20\end{array}\right][/tex]
∵ The dimensions of D are 3 × 2
∵ The corresponding elements of A and D are equal
∴ A and D are equal matrices
