If A = begin{bmatrix} -1 & 0 0 & 2 end{bmatr | vedclass

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

Question

(A) Given that,$A = \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bmatrix}$.First,we calculate $A^2$:$A^2 = A \cdot A = \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bm

Vedclass · Accepted Answer

$2A$

Vedclass · Answer

(A) Given that,$A = \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bmatrix}$.First,we calculate $A^2$:$A^2 = A \cdot A = \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bmatrix} \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bmatrix} = \begin{bmatrix} (-1)(-1) + (0)(0) & (-1)(0) + (0)(2) \ (0)(-1) + (2)(0) & (0)(0) + (2)(2) \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 0 & 4 \end{bmatrix}$.Next,we calculate $A^3$:$A^3 = A^2 \cdot A = \begin{bmatrix} 1 & 0 \ 0 & 4 \end{bmatrix} \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bmatrix} = \begin{bmatrix} (1)(-1) + (0)(0) & (1)(0) + (0)(2) \ (0)(-1) + (4)(0) & (0)(0) + (4)(2) \end{bmatrix} = \begin{bmatrix} -1 & 0 \ 0 & 8 \end{bmatrix}$.Now,calculate $A^3 - A^2$:$A^3 - A^2 = \begin{bmatrix} -1 & 0 \ 0 & 8 \end{bmatrix} - \begin{bmatrix} 1 & 0 \ 0 & 4 \end{bmatrix} = \begin{bmatrix} -1 - 1 & 0 - 0 \ 0 - 0 & 8 - 4 \end{bmatrix} = \begin{bmatrix} -2 & 0 \ 0 & 4 \end{bmatrix}$.We observe that $2A = 2 \begin{bmatrix} -1 & 0 \ 0 & 2 \end{bmatrix} = \begin{bmatrix} -2 & 0 \ 0 & 4 \end{bmatrix}$.Therefore,$A^3 - A^2 = 2A$.

If $A = \begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix}$,then $A^3 - A^2$ is equal to

Similar Questions

Two soap bubbles combine to form a single bubble. In this process, the change in volume and surface area are respectively $V$ and $A$. If $P$ is the atmospheric pressure, and $T$ is the surface tension of the soap solution, the following relation is true :

Diazo-coupling is useful to prepare some

$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. If the central region of the lens with diameter $\frac{d}{2}$ is covered by black paper,what will be the new focal length and intensity of the image,respectively?

Which of the following isomerism is not possible for complexes having molecular formulae?
$(I) Pt(SCN)_2 \cdot 3PEt_3$,$(II) CoBr \cdot SO_4 \cdot 5NH_3$,$(III) FeCl_2 \cdot 6H_2O$

What product is obtained when ethyl hydrogen sulphate is heated with an excess of alcohol at $410 \, K$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module