Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine the values of [tex]\( m \)[/tex] and [tex]\( n \)[/tex] in the given matrix addition problem, we need to add the corresponding elements of the two matrices on the left side of the equation and set them equal to the corresponding elements in the resulting matrix on the right side.
Given the equation:
[tex]\[ \left[\begin{array}{cc} n-1 & 6 \\ -19 & m+3 \end{array}\right]+\left[\begin{array}{cc} -1 & 0 \\ 16 & -8 \end{array}\right]=\left[\begin{array}{cc} 10 & 6 \\ -3 & 40 \end{array}\right] \][/tex]
Let's add the matrices element by element:
1. For the element in the first row, first column:
[tex]\[ (n - 1) + (-1) = 10 \][/tex]
Simplifying:
[tex]\[ n - 1 - 1 = 10 \][/tex]
[tex]\[ n - 2 = 10 \][/tex]
Adding 2 to both sides:
[tex]\[ n = 12 \][/tex]
2. For the element in the first row, second column:
[tex]\[ 6 + 0 = 6 \][/tex]
This agrees with the element in the resulting matrix.
3. For the element in the second row, first column:
[tex]\[ -19 + 16 = -3 \][/tex]
This agrees with the element in the resulting matrix.
4. For the element in the second row, second column:
[tex]\[ (m + 3) + (-8) = 40 \][/tex]
Simplifying:
[tex]\[ m + 3 - 8 = 40 \][/tex]
[tex]\[ m - 5 = 40 \][/tex]
Adding 5 to both sides:
[tex]\[ m = 45 \][/tex]
Therefore, the values of [tex]\( m \)[/tex] and [tex]\( n \)[/tex] are:
[tex]\( m = 45 \)[/tex]
[tex]\( n = 12 \)[/tex]
Given the equation:
[tex]\[ \left[\begin{array}{cc} n-1 & 6 \\ -19 & m+3 \end{array}\right]+\left[\begin{array}{cc} -1 & 0 \\ 16 & -8 \end{array}\right]=\left[\begin{array}{cc} 10 & 6 \\ -3 & 40 \end{array}\right] \][/tex]
Let's add the matrices element by element:
1. For the element in the first row, first column:
[tex]\[ (n - 1) + (-1) = 10 \][/tex]
Simplifying:
[tex]\[ n - 1 - 1 = 10 \][/tex]
[tex]\[ n - 2 = 10 \][/tex]
Adding 2 to both sides:
[tex]\[ n = 12 \][/tex]
2. For the element in the first row, second column:
[tex]\[ 6 + 0 = 6 \][/tex]
This agrees with the element in the resulting matrix.
3. For the element in the second row, first column:
[tex]\[ -19 + 16 = -3 \][/tex]
This agrees with the element in the resulting matrix.
4. For the element in the second row, second column:
[tex]\[ (m + 3) + (-8) = 40 \][/tex]
Simplifying:
[tex]\[ m + 3 - 8 = 40 \][/tex]
[tex]\[ m - 5 = 40 \][/tex]
Adding 5 to both sides:
[tex]\[ m = 45 \][/tex]
Therefore, the values of [tex]\( m \)[/tex] and [tex]\( n \)[/tex] are:
[tex]\( m = 45 \)[/tex]
[tex]\( n = 12 \)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.