At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To calculate the product, we need to perform a step-by-step multiplication of matrix [tex]\( A \)[/tex] by 5, and then verify the matrices involved. Let's start by addressing the components provided:
1. The product of 5 with matrix [tex]\( A \)[/tex]:
[tex]\[ 5\left[\begin{array}{ccc} 2 & 3 & 4 \\ 9 & -1 & -7 \\ 11 & 5 & -3 \end{array}\right] = \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
The operation of multiplying 5 with each element of matrix [tex]\( A \)[/tex] results in:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
This confirms matrix [tex]\( B \)[/tex] as:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
2. Given matrices:
- The first matrix given is:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
Which matches the matrix [tex]\( B \)[/tex].
- The second matrix given is:
[tex]\[ \left[\begin{array}{ccc} 10 & 3 & 4 \\ 45 & -1 & -7 \\ 55 & 5 & -3 \end{array}\right] \][/tex]
Which is a different transformation of the elements of matrix [tex]\( A \)[/tex].
- The third matrix given is:
[tex]\[ \left[\begin{array}{ccc} 7 & 8 & 9 \\ 14 & 4 & -2 \end{array}\right] \][/tex]
Taking into account all given information, we summarize the matrices transformations and products as follows:
- The first step is computing 5 times matrix [tex]\( A \)[/tex].
- The second step is identifying the given matrices and comparing them with our computed results.
Final results for all matrix computations are:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right], \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right], \left[\begin{array}{ccc} 10 & 3 & 4 \\ 45 & -1 & -7 \\ 55 & 5 & -3 \end{array}\right], \left[\begin{array}{ccc} 7 & 8 & 9 \\ 14 & 4 & -2 \end{array}\right] \][/tex]
1. The product of 5 with matrix [tex]\( A \)[/tex]:
[tex]\[ 5\left[\begin{array}{ccc} 2 & 3 & 4 \\ 9 & -1 & -7 \\ 11 & 5 & -3 \end{array}\right] = \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
The operation of multiplying 5 with each element of matrix [tex]\( A \)[/tex] results in:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
This confirms matrix [tex]\( B \)[/tex] as:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
2. Given matrices:
- The first matrix given is:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right] \][/tex]
Which matches the matrix [tex]\( B \)[/tex].
- The second matrix given is:
[tex]\[ \left[\begin{array}{ccc} 10 & 3 & 4 \\ 45 & -1 & -7 \\ 55 & 5 & -3 \end{array}\right] \][/tex]
Which is a different transformation of the elements of matrix [tex]\( A \)[/tex].
- The third matrix given is:
[tex]\[ \left[\begin{array}{ccc} 7 & 8 & 9 \\ 14 & 4 & -2 \end{array}\right] \][/tex]
Taking into account all given information, we summarize the matrices transformations and products as follows:
- The first step is computing 5 times matrix [tex]\( A \)[/tex].
- The second step is identifying the given matrices and comparing them with our computed results.
Final results for all matrix computations are:
[tex]\[ \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right], \left[\begin{array}{ccc} 10 & 15 & 20 \\ 45 & -5 & -35 \\ 55 & 25 & -15 \end{array}\right], \left[\begin{array}{ccc} 10 & 3 & 4 \\ 45 & -1 & -7 \\ 55 & 5 & -3 \end{array}\right], \left[\begin{array}{ccc} 7 & 8 & 9 \\ 14 & 4 & -2 \end{array}\right] \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.