The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are defined. A is 4 × 2, B is 2 × 4.

The size of a matrix is its dimension,

The size of AB and BA are 4 x 4 and 2 x 2, respectively

The dimension of matrix A is given as 4 x 2, while the dimension of matrix B is  2 x 4

Product AB

The dimension of matrix AB is the row of matrix A by the column of matrix B.

Matrix A has 4 rows, while matrix B has 4 columns.

So, the dimension of matrix AB is 4 x 4

Product BA

The dimension of matrix BA is the row of matrix B by the column of matrix A.

Matrix B has 2 rows, while matrix A has 2 columns.

So, the dimension of matrix BA is 2 x 2

Hence, the size of AB and BA are 4 x 4 and 2 x 2, respectively

Read more about matrices at:

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AB: size 4 x 4

BA: size 2 x 2

Step-by-step explanation:

When we want to multiply two matrices, we need first to check if the number of columns of the first matrix is equal the number of rows of the second matrix. Then, the resulting matrix would have the number of rows equal the number of rows of the first matrix, and the number of columns equal the number of columns of the second matrix.

That is, if we have a matrix A with dimensions a x b and a matrix B with dimensions c x d, to calculate the product AB we must have b = c, and the resulting product would have dimensions a x d.

Finally, if A is 4 x 2 and B is 2 x 4, we would have:

AB = (4 x 2) (2 x 4)

2 = 2 -> product is possible.

Dimensions of the result: 4 x 4

BA = (2 x 4) (4 x 2)

4 = 4 -> product is possible.

Dimensions of the result: 2 x 2

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.