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Mathematics

Grade9

Easy

Question

Multiply: $A equals open square brackets table attributes columnalign left end attributes row 1 0 row 0 1 end table close square brackets space B equals open square brackets table attributes columnalign left end attributes row 1 1 row 1 1 end table close square brackets$

$[\begin{array}{l} 1 & 1 \\ 1 & 0 \end{array}]$
$[\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$
$[\begin{array}{l} 0 & 1 \\ 1 & 1 \end{array}]$
$[\begin{array}{l} 1 & 1 \\ 1 & 1 \end{array}]$

hint Hint:

We can understand the general process of matrix multiplication by the technique, "First rows are multiplied by columns (element by element) and then the rows are filled up. Multiplying matrices can be performed using the following steps:
Step 1: Make sure that the number of columns in the 1^st matrix equals the number of rows in the 2^nd matrix (compatibility of matrices).
Step 2: Multiply the elements of i^th row of the first matrix by the elements of j^thcolumn in the second matrix and add the products. This would the element that is in the i^th row and j^th column of the resultant matrix.
Step 3: Place the added products in the respective positions.

The correct answer is: $open square brackets table attributes columnalign left end attributes row 1 1 row 1 1 end table close square brackets$

$A equals open square brackets table attributes columnalign left end attributes row 1 0 row 0 1 end table close square brackets comma space B equals open square brackets table attributes columnalign left end attributes row 1 1 row 1 1 end table close square brackets$
We can understand the general process of matrix multiplication by the technique, "First rows are multiplied by columns (element by element) and then the rows are filled up. Multiplying matrices can be performed using the following steps:
Step 1: Make sure that the number of columns in the 1st matrix equals the number of rows in the 2nd matrix (compatibility of matrices).
$A equals open square brackets table attributes columnalign left end attributes row 1 0 row 0 1 end table close square brackets comma space C o l u m n s space equals space 2 space B equals open square brackets table attributes columnalign left end attributes row 1 1 row 1 1 end table close square brackets comma space R o w s space equals space 2$
Step 2: Multiply the elements of ith row of the first matrix by the elements of jth column in the second matrix and add the products. This would the element that is in the ith row and jth column of the resultant matrix.
$A space cross times space B space equals space open square brackets table attributes columnalign left end attributes row 1 0 row 0 1 end table close square brackets cross times open square brackets table attributes columnalign left end attributes row 1 1 row 1 1 end table close square brackets equals open square brackets table attributes columnalign left end attributes row cell 1 cross times 1 plus 0 cross times 1 end cell cell 1 cross times 1 plus 0 cross times 1 end cell row cell 0 cross times 1 plus 1 cross times 1 end cell cell 0 cross times 1 plus 1 cross times 1 end cell end table close square brackets$
Step 3: Place the added products in the respective positions.
$A cross times B equals open square brackets table attributes columnalign left end attributes row cell 1 cross times 1 plus 0 cross times 1 end cell cell 1 cross times 1 plus 0 cross times 1 end cell row cell 0 cross times 1 plus 1 cross times 1 end cell cell 0 cross times 1 plus 1 cross times 1 end cell end table close square brackets space equals space open square brackets table attributes columnalign left end attributes row 1 1 row 1 1 end table close square brackets$

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