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Ksivusya [100]
3 years ago
11

Inverse this matrix

Mathematics
1 answer:
SIZIF [17.4K]3 years ago
6 0
In order for the inverse to exist, the matrix cannot be singular, so we need to first examine the conditions for existence of the inverse.

Compute the determinant. The easiest way might be a cofactor expansion along either the first row or third column; I'll do the first.

\begin{vmatrix}x&0&0\\0&1&0\\w&0&x\end{vmatrix}=x\begin{vmatrix}1&0\\0&x\end{vmatrix}=x^2

The matrix is then singular whenever x\neq0.

With this in mind, compute the inverse.

\mathbf A=\begin{bmatrix}x&0&0\\0&1&0\\w&0&x\end{bmatrix}\implies\mathbf A^{-1}=\dfrac1{x^2}\begin{bmatrix}a&0&-w\\0&-x^2&0\\0&0&x\end{bmatrix}=\begin{bmatrix}\frac a{x^2}&0&-\frac w{x^2}\\0&-1&0\\0&0&\frac1x\end{bmatrix}
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The number of visits to public libraries increased from 1.5 billion in 1991 to 1.7 billion in 1996. Find the average rate of cha
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6 0
1 year ago
Michael Pedro and Kevin were saving money. All together they saved $130. Kevin saved 3 times more than Pedro. Michael saved $20
yKpoI14uk [10]

Answer:

The saving of all three person are

The Pedro's saving is $ 30

The Michael's saving is $ 10

The Kevin's saving is $ 90

Step-by-step explanation:

Given as :

The three person namely Michael , Pedro , Kevin

The total saving of all together = $ 130

Let The Michael's saving = $ M

The Pedro's saving = $ P

The Kevin's saving = $ k

I.e Michael's saving + Pedro's saving + Kevin's saving = $ 130

Or, M + P + K = $ 130

again ,

Kevin saved 3 times more than Pedro

I.e K = 3 × P

And , Michael save $ 20 less than Pedro

I.e M = P - $ 20

Now

∵ M + P + K = $ 130

or, (  P - $ 20) + P + 3 × P = $ 130

Or, 5 P - $ 20 = $ 130

Or, 5 P = $ 130 + $ 20

Or, 5 P = $ 150

∴ P = $ \frac{150}{5}

I.e P = $ 30

So The Pedro's saving = P = $ 30

And

M = P - $ 20

∴, M = $ 30 - $ 20

I.e M = $ 10

So,  The Michael's saving = M = $ 10

Similarly

K = 3 × P

∴ k = 3 × $ 30

I.e K = $ 90

So, The Kevin's saving = k = $ 90

Hence The saving of all three person are

The Pedro's saving is $ 30

The Michael's saving is $ 10

The Kevin's saving is $ 90

Answer

5 0
3 years ago
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