Answer:
a=
⇒ 3.5
b=
⇒ 1.5
c=
⇒ -1.5
d=
⇒ 6.5
e=
⇒ 1.5 f=
⇒ -2.5
g=
⇒ -8.5
h=
⇒ -2.5
i=
⇒ 3.5
Step-by-step explanation:
The values of the a, b, c, d, e, f, g, h, and i can be calculated after finding the inverse of a matrix.
It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.
We have a matrix A shown in the picture:
| 2 3 3 |
A = | 3 1 2 |
| 7 8 9 |
It is required to find the inverses of a matrix.
To find the inverse of a matrix:
Augment with a 3x3 identity matrix
[tex]=\begin{bmatrix}2&3&3&\mid \:&1&0&0\\ 3&1&2&\mid \:&0&1&0\\ 7&8&9&\mid \:&0&0&1\end{bmatrix}[/tex]
Convert the matrix to the identity matrix.
[tex]=\begin{bmatrix}1&0&0&\mid \:&\frac{7}{2}&\frac{3}{2}&-\frac{3}{2}\\ 0&1&0&\mid \:&\frac{13}{2}&\frac{3}{2}&-\frac{5}{2}\\ 0&0&1&\mid \:&-\frac{17}{2}&-\frac{5}{2}&\frac{7}{2}\end{bmatrix}[/tex]
Simply it:
[tex]=\begin{pmatrix}\dfrac{7}{2}&\dfrac{3}{2}&-\dfrac{3}{2}\\ \dfrac{13}{2}&\dfrac{3}{2}&-\dfrac{5}{2}\\ -\dfrac{17}{2}&-\dfrac{5}{2}&\dfrac{7}{2}\end{pmatrix}[/tex]
From the inverse matrix the values of unknows can be find:
a = 7/2
b = 3/2
c = -3/2
d = 13/2
e = 3/2
f = -5/2
g = -17/2
h = -5/2
i = 7/2
Thus, the values of the a, b, c, d, e, f, g, h, and i can be calculated after finding the inverse of a matrix.
Learn more about the matrix here:
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