If S= 	
–
1	4
–
5	0
8	3
  and q=
–
6, what is qS?
If the matrix exists, select its size before entering your answer. If the matrix does not exist, select undefined.

Given that \( S \) is a 3x2 matrix and \( q \) is a scalar value (6), we can compute the product \( qS \) by multiplying each element of the matrix \( S \) by the scalar \( q \).

The matrix \( S \) is:

\[
S = \begin{pmatrix} 
-1 & 4 \\ 
-5 & 0 \\ 
8 & 3 
\end{pmatrix}
\]

Multiplying each element of \( S \) by \( q = 6 \), we get:

\[
qS = 6 \times \begin{pmatrix} 
-1 & 4 \\ 
-5 & 0 \\ 
8 & 3 
\end{pmatrix}
= \begin{pmatrix} 
6 \times (-1) & 6 \times 4 \\ 
6 \times (-5) & 6 \times 0 \\ 
6 \times 8 & 6 \times 3 
\end{pmatrix}
= \begin{pmatrix} 
-6 & 24 \\ 
-30 & 0 \\ 
48 & 18 
\end{pmatrix}
\]

Thus, the product \( qS \) is:

\[
qS = \begin{pmatrix} 
-6 & 24 \\ 
-30 & 0 \\ 
48 & 18 
\end{pmatrix}
\]

The size of the resulting matrix is 3x2, which is the same as the original matrix \( S \).

Do you want further details or have any questions?

Here are some related questions:
1. How do we multiply a scalar with a matrix?
2. What happens if we multiply two matrices together?
3. How can you find the transpose of a matrix?
4. Can a scalar multiplication result in a different matrix size?
5. What is the identity matrix and its role in matrix multiplication?

**Tip:** Matrix dimensions are critical in determining if operations like multiplication are valid. Always verify the sizes!

If S= – 1 4 – 5 0 8 3 and q= – 6, what is qS? If the matrix exists, select its size before entering your answer. If the matrix does not exist, select undefined.

Discover how to perform scalar multiplication by multiplying a 3x2 matrix S by scalar q = -6. This problem covers key matrix algebra concepts and explains the step-by-step process of multiplying a matrix by a scalar. Ideal for students in Grades 10-12.

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