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Math  /  Algebra

QuestionFind the product, if possible. [15−5][15−8−4−15]\left[\begin{array}{r} 1 \\ 5 \\ -5 \end{array}\right]\left[\begin{array}{rrr} 1 & 5 & -8 \\ -4 & -1 & 5 \end{array}\right]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The product is □\square B. The product is not defined.

Studdy Solution

STEP 1

1. We are given two matrices and need to determine if their product is defined.
2. Matrix multiplication is only possible when the number of columns in the first matrix equals the number of rows in the second matrix.

STEP 2

1. Determine the dimensions of both matrices.
2. Check if the product is defined based on matrix multiplication rules.
3. If defined, calculate the product.

STEP 3

Determine the dimensions of the first matrix:
The first matrix is: [15−5]\left[\begin{array}{r} 1 \\ 5 \\ -5 \end{array}\right]
This is a column matrix with 3 rows and 1 column, so its dimensions are 3×13 \times 1.

STEP 4

Determine the dimensions of the second matrix:
The second matrix is: [15−8−4−15]\left[\begin{array}{rrr} 1 & 5 & -8 \\ -4 & -1 & 5 \end{array}\right]
This is a matrix with 2 rows and 3 columns, so its dimensions are 2×32 \times 3.

STEP 5

Check if the product is defined:
For matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix. Here, the first matrix has 1 column, and the second matrix has 2 rows. Since 1≠21 \neq 2, the product is not defined.
The correct choice is:
B. The product is not defined.

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