Determine whether the product is defined or undefined. If defined, give the dimensions of the product matrix.
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A: defined; 2 x 2
B: defined; 2 x 1
C: defined; 1 x 2
D: undefined
Well, I don't usually deal with serious stuff, but let's give it a shot. To determine if the product is defined, we need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix. Let's count those little critters. The first matrix has 2 columns, and the second matrix has 2 rows. Ah-ha! They match!
So, the product is defined! Now, let's talk dimensions. The first matrix is a 2 x 2 matrix, and the second matrix is a 2 x 1 matrix. When we multiply these two together, we get a 2 x 1 matrix as a result. So, the dimensions of the product matrix are 2 x 1.
That means the answer is B: defined; 2 x 1. It's like solving a good old-fashioned riddle, right?
To determine whether the product of two matrices is defined, we need to make sure that the number of columns in the first matrix is equal to the number of rows in the second matrix.
In this case, the first matrix has two columns, and the second matrix has two rows. Since the number of columns in the first matrix matches the number of rows in the second matrix, the product is defined.
To find the dimensions of the product matrix, we take the number of rows from the first matrix and the number of columns from the second matrix. In this case, the first matrix has 2 rows, and the second matrix has 1 column. Therefore, the dimensions of the product matrix are 2 x 1.
So, the correct answer is B: defined; 2 x 1.
To determine whether the product is defined or undefined, we need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix.
The first matrix has 2 columns and the second matrix has 1 row.
Since the number of columns in the first matrix does not equal the number of rows in the second matrix, the product is undefined.
Therefore, the answer is D: undefined.