CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Nilpotent Matrix

If A= [ 1 -3 ...

Question

If $A = [\begin{matrix} 1 & - 3 & 2 2 & 0 & 2 \end{matrix}]$ and $B = [\begin{matrix} 2 & - 1 & - 1 1 & 0 & - 1 \end{matrix}]$ , then the matrix $C$ such that $A + B + C$ is a zero matrix, is

Open in App

Solution

$A + B + C = O$
$\Rightarrow C = - A - B$
$\Rightarrow C = - [\begin{matrix} 1 & - 3 & 2 2 & 0 & 2 \end{matrix}] - [\begin{matrix} 2 & - 1 & - 1 1 & 0 & - 1 \end{matrix}]$

$\Rightarrow C = [\begin{matrix} - 1 - 2 & 3 + 1 & - 2 + 1 - 2 - 1 & 0 - 0 & - 2 + 1 \end{matrix}]$

$\Rightarrow C = [\begin{matrix} - 3 & 4 & - 1 - 3 & 0 & - 1 \end{matrix}]$

Suggest Corrections

thumbs-up

0

Similar questions

[\begin{matrix} 1 & - 3 & 2 \\ 2 & 0 & 2 \end{matrix}]

[\begin{matrix} 2 & - 1 & - 1 \\ 1 & 0 & - 1 \end{matrix}]

, find the matrix C such that A + B + C is zero matrix.

A = ⎡ ⎢ ⎣ \begin{matrix} 151 \end{matrix} \begin{matrix} 20 - 1 \end{matrix} \begin{matrix} - 3 21 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 342 \end{matrix} \begin{matrix} - 1 20 \end{matrix} \begin{matrix} 253 \end{matrix} ⎤ ⎥ ⎦

C = ⎡ ⎢ ⎣ \begin{matrix} 401 \end{matrix} \begin{matrix} 13 - 2 \end{matrix} \begin{matrix} 223 \end{matrix} ⎤ ⎥ ⎦

(A + B)

(B - C)

Also, verify that

A + (B - C) = (A + B) - C

\"[\"\begin{matrix} 1 & - 3 & 2 \\ 2 & 0 & 2 \end{matrix}\"]\"

\"[\"\begin{matrix} 2 & - 1 & - 1 \\ 1 & 0 & - 1 \end{matrix}\"]\"

, find the matrix C such that A + B + C is zero matrix.

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 2 - 3 & 1 4 & 0 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 6 & 2 1 & 3 0 & 4 \end{matrix} ⎤ ⎥ ⎦

C

A + B + C = O

O

is the zero matrix.

a \neq b \neq c

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{3} - 1 & b^{3} - 1 & c^{3} - 1 a & b & c a^{2} & b^{2} & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Nilpotent Matrix

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon