3. solve the matrix expression\n2\\begin{bmatrix}1&2\\3&4\\end{bmatrix}+3\\begin{bmatrix}2&1\\…

3. solve the matrix expression\n2\\begin{bmatrix}1&2\\3&4\\end{bmatrix}+3\\begin{bmatrix}2&1\\ - 1&-2\\end{bmatrix}=?\nshow your work.\n4. given that\nx - y = 7\n2y+3x = 36\ndetermine the value of x + y. show your work.\nx = \n\ny = \n\nx + y=\n

3. solve the matrix expression\n2\\begin{bmatrix}1&2\\3&4\\end{bmatrix}+3\\begin{bmatrix}2&1\\ - 1&-2\\end{bmatrix}=?\nshow your work.\n4. given that\nx - y = 7\n2y+3x = 36\ndetermine the value of x + y. show your work.\nx = \n\ny = \n\nx + y=\n

Answer

Explanation:

Step1: Multiply first matrix by 2

$\begin{bmatrix} 2\times1 & 2\times2 \ 2\times3 & 2\times4 \end{bmatrix} = \begin{bmatrix} 2 & 4 \ 6 & 8 \end{bmatrix}$

Step2: Multiply second matrix by 3

$\begin{bmatrix} 3\times2 & 3\times1 \ 3\times(-1) & 3\times(-2) \end{bmatrix} = \begin{bmatrix} 6 & 3 \ -3 & -6 \end{bmatrix}$

Step3: Add the two matrices

$\begin{bmatrix} 2+6 & 4+3 \ 6+(-3) & 8+(-6) \end{bmatrix} = \begin{bmatrix} 8 & 7 \ 3 & 2 \end{bmatrix}$

Explanation:

Step1: Express x from first equation

$x = y + 7$

Step2: Substitute x into second equation

$2y + 3(y + 7) = 36$

Step3: Solve for y

$5y + 21 = 36 \implies 5y = 15 \implies y = 3$

Step4: Find x

$x = 3 + 7 = 10$

Step5: Calculate x + y

$x + y = 10 + 3 = 13$

Answer:

$\begin{bmatrix} 8 & 7 \ 3 & 2 \end{bmatrix}$ x = 10 y = 3 x + y = 13