If A = begin{bmatrix} 1 & -2 4 & 5 end{bmatr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $A = \begin{bmatrix} 1 & -2 \ 4 & 5 \end{bmatrix}$ and $f(t) = t^2 - 3t + 7$.First, calculate $A^2$:$A^2 = \begin{bmatrix} 1 & -2 \ 4 & 5

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given $A = \begin{bmatrix} 1 & -2 \ 4 & 5 \end{bmatrix}$ and $f(t) = t^2 - 3t + 7$.First, calculate $A^2$:$A^2 = \begin{bmatrix} 1 & -2 \ 4 & 5 \end{bmatrix} \begin{bmatrix} 1 & -2 \ 4 & 5 \end{bmatrix} = \begin{bmatrix} 1(1) + (-2)(4) & 1(-2) + (-2)(5) \ 4(1) + 5(4) & 4(-2) + 5(5) \end{bmatrix} = \begin{bmatrix} -7 & -12 \ 24 & 17 \end{bmatrix}$.Now, calculate $f(A) = A^2 - 3A + 7I$, where $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$:$f(A) = \begin{bmatrix} -7 & -12 \ 24 & 17 \end{bmatrix} - 3 \begin{bmatrix} 1 & -2 \ 4 & 5 \end{bmatrix} + 7 \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$$f(A) = \begin{bmatrix} -7 & -12 \ 24 & 17 \end{bmatrix} - \begin{bmatrix} 3 & -6 \ 12 & 15 \end{bmatrix} + \begin{bmatrix} 7 & 0 \ 0 & 7 \end{bmatrix}$$f(A) = \begin{bmatrix} -7-3+7 & -12+6+0 \ 24-12+0 & 17-15+7 \end{bmatrix} = \begin{bmatrix} -3 & -6 \ 12 & 9 \end{bmatrix}$.Finally, calculate $f(A) + \begin{bmatrix} 3 & 6 \ -12 & -9 \end{bmatrix}$:$\begin{bmatrix} -3 & -6 \ 12 & 9 \end{bmatrix} + \begin{bmatrix} 3 & 6 \ -12 & -9 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$.

If $A = \begin{bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t) = t^2 - 3t + 7$, then $f(A) + \begin{bmatrix} 3 & 6 \\ -12 & -9 \end{bmatrix}$ is equal to

Similar Questions

The matrix $\begin{bmatrix} 2 & 5 & -7 \\ 0 & 3 & 11 \\ 0 & 0 & 9 \end{bmatrix}$ is known as:

If the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2 \end{bmatrix}$, then $A^n = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ b & 0 & a \end{bmatrix}$, for $n \in N$, where:

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} x & y \\ 0 & x \end{bmatrix}$,then $AB = BA$ (given $B \neq I$). Which of the following matrices $B$ satisfies this condition?

If $x \begin{bmatrix} 2 \\ 3 \end{bmatrix} + y \begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix}$,find the values of $x$ and $y$.

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$,then prove that $A^{n} = \begin{bmatrix} \cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta \end{bmatrix}$ for all $n \in N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module