Question

If t is an identity matrix of order 3, then t2 + 2t is equal to



a. T



b. 2t



c. 3t



d. 4t brainly

Answer 1

Answer:

Option C is correct.

Step-by-step explanation:

$Identity\:Matrix\:of\:order\:3\:,t\:=\:\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

We need to find value of t² + 2t

First we find t²,

$t^2=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\times\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

$=\begin{bmatrix}1\times1+0\times0+0\times0&1\times0+0\times1+0\times0&1\times0+0\times0+0\times1\\0\times1+1\times0+0\times0&0\times0+1\times1+0\times0&0\times0+1\times0+0\times1\\0\times1+0\times0+1\times0&0\times0+0\times1+1\times0&0\times0+0\times0+1\times1\end{bmatrix}$

$=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

So, t² = t

Now, t² + 2t = t + 2t = 3t

Therefore, Option C is correct.