Question

[3/4]*[4/8] plz solve matrix​

Answer 1

Step-by-step explanation:

The "Dot Product" is where we multiply matching members, then sum up:

(1, 2, 3) • (7, 9, 11) = 1×7 + 2×9 + 3×11

= 58

We match the 1st members (1 and 7), multiply them, likewise for the 2nd members (2 and 9) and the 3rd members (3 and 11), and finally sum them up.

Want to see another example? Here it is for the 1st row and 2nd column:

Matrix Multiply next entry

(1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12

= 64

We can do the same thing for the 2nd row and 1st column:

(4, 5, 6) • (7, 9, 11) = 4×7 + 5×9 + 6×11

= 139

And for the 2nd row and 2nd column:

(4, 5, 6) • (8, 10, 12) = 4×8 + 5×10 + 6×12

= 154

And we get:

Matrix Multiply Finished

DONE!

Why Do It This Way?

This may seem an odd and complicated way of multiplying, but it is necessary!

I can give you a real-life example to illustrate why we multiply matrices in this way.

Example: The local shop sells 3 types of pies.

Apple pies cost $3 each

Cherry pies cost $4 each

Blueberry pies cost $2 each

And this is how many they sold in 4 days:

Matrix Multiply Table

Now think about this ... the value of sales for Monday is calculated this way:

Apple pie value + Cherry pie value + Blueberry pie value

$3×13 + $4×8 + $2×6 = $83

So it is, in fact, the "dot product" of prices and how many were sold:

($3, $4, $2) • (13, 8, 6) = $3×13 + $4×8 + $2×6

= $83

We match the price to how many sold, multiply each, then sum the result.

In other words:

The sales for Monday were: Apple pies: $3×13=$39, Cherry pies: $4×8=$32, and Blueberry pies: $2×6=$12. Together that is $39 + $32 + $12 = $83

And for Tuesday: $3×9 + $4×7 + $2×4 = $63

And for Wednesday: $3×7 + $4×4 + $2×0 = $37

And for Thursday: $3×15 + $4×6 + $2×3 = $75

So it is important to match each price to each quantity.

Now you know why we use the "dot product".

And here is the full result in Matrix form:

Matrix Multiply

They sold $83 worth of pies on Monday, $63 on Tuesday, etc.

(You can put those values into the Matrix Calculator to see if they work.)

Rows and Columns

To show how many rows and columns a matrix has we often write rows×columns.

Example: This matrix is 2×3 (2 rows by 3 columns):

2x3 Matrix

When we do multiplication:

The number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.

And the result will have the same number of rows as the 1st matrix, and the same number of columns as the 2nd matrix.

Example:

Matrix Multiply

In that example we multiplied a 1×3 matrix by a 3×4 matrix (note the 3s are the same), and the result was a 1×4 matrix.

✪============♡============✿

$\huge \pink{✿} \red {C} \green {u} \blue {t} \orange {e} \pink {/} \red {Q} \blue {u} \pink {e} \red {e} \green {n} \pink {♡}$

Answer 2

Step-by-step explanation:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99.