Discover new knowledge and insights with IDNLearn.com's extensive Q&A platform. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.
Sagot :
Let's solve the given matrix expression step-by-step.
We have the expression:
[tex]\[ \left[\begin{array}{cr}1 & -2 \\ -3 & 4 \\ 5 & 3\end{array}\right] + 2\left[\begin{array}{ll}0 & 1 \\ 6 & 7 \\ 5 & 0\end{array}\right] \][/tex]
First, let's define the matrices [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[ A = \left[\begin{array}{cr}1 & -2 \\ -3 & 4 \\ 5 & 3\end{array}\right] \][/tex]
[tex]\[ B = \left[\begin{array}{ll}0 & 1 \\ 6 & 7 \\ 5 & 0\end{array}\right] \][/tex]
Next, we need to perform scalar multiplication on matrix [tex]\(B\)[/tex] with the scalar [tex]\(2\)[/tex]:
[tex]\[ 2 \times B = 2 \times \left[\begin{array}{ll}0 & 1 \\ 6 & 7 \\ 5 & 0\end{array}\right] = \left[\begin{array}{ll}2 \times 0 & 2 \times 1 \\ 2 \times 6 & 2 \times 7 \\ 2 \times 5 & 2 \times 0\end{array}\right] = \left[\begin{array}{ll}0 & 2 \\ 12 & 14 \\ 10 & 0\end{array}\right] \][/tex]
So, multiplying matrix [tex]\(B\)[/tex] by [tex]\(2\)[/tex] gives us:
[tex]\[ 2B = \left[\begin{array}{ll}0 & 2 \\ 12 & 14 \\ 10 & 0\end{array}\right] \][/tex]
Now, we need to add the matrices [tex]\(A\)[/tex] and [tex]\(2B\)[/tex]:
[tex]\[ A + 2B = \left[\begin{array}{cr}1 & -2 \\ -3 & 4 \\ 5 & 3\end{array}\right] + \left[\begin{array}{ll}0 & 2 \\ 12 & 14 \\ 10 & 0\end{array}\right] \][/tex]
We perform the addition element-wise:
[tex]\[ \left[\begin{array}{cr}1 + 0 & -2 + 2 \\ -3 + 12 & 4 + 14 \\ 5 + 10 & 3 + 0\end{array}\right] \][/tex]
Calculating each element, we get:
[tex]\[ \left[\begin{array}{cr}1 & 0 \\ 9 & 18 \\ 15 & 3\end{array}\right] \][/tex]
Thus, the result of the matrix expression is:
[tex]\[ \left[\begin{array}{cr}1 & 0 \\ 9 & 18 \\ 15 & 3\end{array}\right] \][/tex]
We have the expression:
[tex]\[ \left[\begin{array}{cr}1 & -2 \\ -3 & 4 \\ 5 & 3\end{array}\right] + 2\left[\begin{array}{ll}0 & 1 \\ 6 & 7 \\ 5 & 0\end{array}\right] \][/tex]
First, let's define the matrices [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[ A = \left[\begin{array}{cr}1 & -2 \\ -3 & 4 \\ 5 & 3\end{array}\right] \][/tex]
[tex]\[ B = \left[\begin{array}{ll}0 & 1 \\ 6 & 7 \\ 5 & 0\end{array}\right] \][/tex]
Next, we need to perform scalar multiplication on matrix [tex]\(B\)[/tex] with the scalar [tex]\(2\)[/tex]:
[tex]\[ 2 \times B = 2 \times \left[\begin{array}{ll}0 & 1 \\ 6 & 7 \\ 5 & 0\end{array}\right] = \left[\begin{array}{ll}2 \times 0 & 2 \times 1 \\ 2 \times 6 & 2 \times 7 \\ 2 \times 5 & 2 \times 0\end{array}\right] = \left[\begin{array}{ll}0 & 2 \\ 12 & 14 \\ 10 & 0\end{array}\right] \][/tex]
So, multiplying matrix [tex]\(B\)[/tex] by [tex]\(2\)[/tex] gives us:
[tex]\[ 2B = \left[\begin{array}{ll}0 & 2 \\ 12 & 14 \\ 10 & 0\end{array}\right] \][/tex]
Now, we need to add the matrices [tex]\(A\)[/tex] and [tex]\(2B\)[/tex]:
[tex]\[ A + 2B = \left[\begin{array}{cr}1 & -2 \\ -3 & 4 \\ 5 & 3\end{array}\right] + \left[\begin{array}{ll}0 & 2 \\ 12 & 14 \\ 10 & 0\end{array}\right] \][/tex]
We perform the addition element-wise:
[tex]\[ \left[\begin{array}{cr}1 + 0 & -2 + 2 \\ -3 + 12 & 4 + 14 \\ 5 + 10 & 3 + 0\end{array}\right] \][/tex]
Calculating each element, we get:
[tex]\[ \left[\begin{array}{cr}1 & 0 \\ 9 & 18 \\ 15 & 3\end{array}\right] \][/tex]
Thus, the result of the matrix expression is:
[tex]\[ \left[\begin{array}{cr}1 & 0 \\ 9 & 18 \\ 15 & 3\end{array}\right] \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.