Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$\begin{bmatrix}8&2a&3\\13&20&7\end{bmatrix}-5\begin{bmatrix}b&-2&-6\\1&4&3c\end{bmatrix}=\begin{bmatrix}-2&3&33\\d&0&-8\end{bmatrix}$[8 2a 313 20 7]−5[b −2 −61 4 3c]=[−2 3 33d 0 −8]$a=$a= , $b=$b= , $c=$c= , $d=$d=
Question
Solve the matrix equation for a, b, c, and d .[8 2a 313 20 7]−5[b −2 −61 4 3c]=[−2 3 33d 0 −8]a= , b= , c= , d=
Solution
To solve the matrix equation, we first need to distribute the scalar -5 to the second matrix. This gives us:
-5 * [b -2 -6; 1 4 3c] = [-5b 10 30; -5 -20 -15c]
Now, we can subtract this matrix from the first matrix to get the right side of the equation:
[8 2a 3; 13 20 7] - [-5b 10 30; -5 -20 -15c] = [8+5b 2a-10 3-30; 13+5 20+20 7+15c]
Setting this equal to the right side of the equation, we get:
[8+5b 2a-10 3-30; 13+5 20+20 7+15c] = [-2 3 33; d 0 -8]
Now, we can equate the corresponding elements in the matrices to get a system of equations:
8 + 5b = -2 => 5b = -2 - 8 => b = -10/5 => b = -2
2a - 10 = 3 => 2a = 3 + 10 => a = 13/2 => a = 6.5
3 - 30 = 33 => -27 = 33 (This is not possible, so there seems to be a mistake in the problem)
13 + 5 = d => d = 18
20 + 20 = 0 => 40 = 0 (This is not possible, so there seems to be a mistake in the problem)
7 + 15c = -8 => 15c = -8 - 7 => c = -15/15 => c = -1
So, the solution to the matrix equation is a = 6.5, b = -2, c = -1, and d = 18. However, there seems to be a mistake in the problem as two of the equations are not possible.
Similar Questions
Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$-3\left(\begin{bmatrix}7&2b\\8c&8\end{bmatrix}-\begin{bmatrix}4&4b\\5&d\end{bmatrix}\right)=\begin{bmatrix}a&54\\63&d\end{bmatrix}$−3([7 2b8c 8]−[4 4b5 d])=[a 5463 d]$a=$a= , $b=$b= , $c=$c= , $d=$d=
Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$\frac{1}{2}$12 $\begin{bmatrix}-6a&-2\\3&14\\-10&-8\end{bmatrix}+\begin{bmatrix}5&3\\-\frac{5}{2}&b-3\\6&-1\end{bmatrix}=\begin{bmatrix}9&4d\\-1&11\\c+4&-5\end{bmatrix}$[−6a −23 14−10 −8]+[5 3−52 b−36 −1]=[9 4d−1 11c+4 −5]$a=$a= , $b=$b= , $c=$c= , $d=$d= Skip to navigationPrevious25, Fully Attempted.26, Fully Attempted.27, Fully Attempted.28, Fully Attempted.29, Fully Attempted.30, Unattempted. Flagged31, Unattempted.32, Unattempted.33, Unattempted.34, Unattempted.Next
Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$\begin{bmatrix}a&b\\3&-4\end{bmatrix}=\begin{bmatrix}6&2\\c&d\end{bmatrix}$[a b3 −4]=[6 2c d]$a=$a= , $b=$b= , $c=$c= , $d=$d=
Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$\begin{bmatrix}7&d\\5&b\end{bmatrix}=\begin{bmatrix}c&4\\a&17\end{bmatrix}$[7 d5 b]=[c 4a 17]$a=$a= , $b=$b= , $c=$c= , $d=$d=
Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$2\left(\begin{bmatrix}3a&11\\4&6\end{bmatrix}+\begin{bmatrix}-7&-6\\11&5d\end{bmatrix}\right)=\begin{bmatrix}22&b\\c&52\end{bmatrix}$2([3a 114 6]+[−7 −611 5d])=[22 bc 52]$a=$a= , $b=$b= , $c=$c= , $d=$d=
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.