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Mathematics

Grade9

Easy

Question

Subtract the matrices: $open square brackets table attributes columnalign left end attributes row 1 2 row 4 5 end table close square brackets comma space open square brackets table attributes columnalign left end attributes row 3 4 row 1 3 end table close square brackets$ .

$[\begin{matrix} 2 & - 2 \\ 3 & 2 \end{matrix}]$
$[\begin{matrix} - 2 & 2 \\ 3 & 2 \end{matrix}]$
$[\begin{matrix} - 2 & - 2 \\ - 3 & 2 \end{matrix}]$
$[\begin{matrix} - 2 & - 2 \\ 3 & 2 \end{matrix}]$

hint Hint:

The subtraction of matrices or matrix subtraction can only be possible if the number of rows and columns of both the matrices are the same. While subtracting two matrices, we subtract the elements in each row and column from the corresponding elements in the row and column of the other matrix.
Consider two matrices A and B of the same order 'm × n', where m is the number of rows and n is the number of columns of the two matrices, denoted as A = [aij] and B = [bij]. Now, the difference of the two matrices A and B is given as: A - B = [aij] - [bij] = [aij - bij], where ij denotes the position of each element in i^th row and j^th column. The dimension of the difference matrix, that is, A - B is also 'm × n'.

The correct answer is: $open square brackets table row cell negative 2 end cell cell negative 2 end cell row 3 2 end table close square brackets$

The subtraction of matrices or matrix subtraction can only be possible if the number of rows and columns of both the matrices are the same. While subtracting two matrices, we subtract the elements in each row and column from the corresponding elements in the row and column of the other matrix.
$A space equals space open square brackets table attributes columnalign left end attributes row 1 2 row 4 5 end table close square brackets comma B space equals space open square brackets table attributes columnalign left end attributes row 3 4 row 1 3 end table close square brackets$

$A space minus space B space equals space open square brackets table attributes columnalign left end attributes row 1 2 row 4 5 end table close square brackets minus open square brackets table attributes columnalign left end attributes row 3 4 row 1 3 end table close square brackets equals open square brackets table attributes columnalign left end attributes row cell 1 minus 3 end cell cell 2 minus 4 end cell row cell 4 minus 1 end cell cell 5 minus 3 end cell end table close square brackets A space minus space B space equals open square brackets table row cell negative 2 end cell cell negative 2 end cell row 3 2 end table close square brackets$

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