A-1 0 0 2 1 0 3 2 1- U1- U2 and U3 are columns matrices satisfying AU1-1 0 0- AU2 - -2 3 0- AU3 - -2 3 1- and U is 3-3 matrix whose columns are U1- U2- U3 then answer the following questionThe sum of elements of U-1 is

The correct option is B 0 U=[ 1 amp;2 amp;2; 2 amp; 1 amp; 1; 1 amp; 4 amp; 3 ] ⇒ |U|= 1 14+18=3 Now, adj U=C^T=[ 1 amp; 7 ...

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

Byju's Answer

Standard XII

Mathematics

Adjoint of a Matrix

A=[1 0 0 2...

Question

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦, U_{1}, U_{2}$ and $U_{3}$ are columns matrices satisfying $A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦, A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦$ and $U$ is $3 \times 3$ matrix whose columns are $U_{1}, U_{2}, U_{3}$ then answer the following question
The sum of elements of $U^{- 1}$ is

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 0
$U = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 2 - 2 & - 1 & - 1 1 & - 4 & - 3 \end{matrix} ⎤ ⎥ ⎦$
$\Rightarrow | U | = - 1 - 14 + 18 = 3$
Now, $a d j U = C^{T} = {⎡ ⎢ ⎣ \begin{matrix} - 1 & - 7 & 9 - 2 & - 5 & 6 0 & - 3 & 3 \end{matrix} ⎤ ⎥ ⎦}^{T}$
$\Rightarrow a d j U = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 2 & 0 - 7 & - 5 & - 3 9 & 6 & 3 \end{matrix} ⎤ ⎥ ⎦$
Hence, $U^{- 1} = \frac{1}{3} ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 2 & 0 - 7 & - 5 & - 3 9 & 6 & 3 \end{matrix} ⎤ ⎥ ⎦$
Now, sum of elements of $U^{- 1} = 0$

Suggest Corrections

Similar questions

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

and

U_{3}

are columns matrices satisfying

A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦, A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦

and

U

3 \times 3

matrix whose columns are

U_{1}, U_{2}, U_{3}

then answer the following question

The value of

| U |

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

and

U_{3}

are columns matrices satisfying

A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦, A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦

and

U

3 \times 3

matrix whose columns are

U_{1}, U_{2}, U_{3}

then answer the following question

The value of

[\begin{matrix} 3 & 2 & 0 \end{matrix}] U ⎡ ⎢ ⎣ \begin{matrix} 320 \end{matrix} ⎤ ⎥ ⎦

Q. Let

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦

and

U_{1}, U_{2}, U_{3}

be column
matrices satisfying

A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦, A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦

. If U is

3 \times 3

matrix whose columns are

U_{1}, U_{2}, U_{3}

, then

| U | =

Q. For a matrix

A ⎛ ⎜ ⎝ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎞ ⎟ ⎠

, if

U_{1}, U_{2}

and

U_{3}

are

3 \times 1

column matrices satisfying

A U_{1} = ⎛ ⎜ ⎝ \begin{matrix} 100 \end{matrix} ⎞ ⎟ ⎠, A U_{2} ⎛ ⎜ ⎝ \begin{matrix} 230 \end{matrix} ⎞ ⎟ ⎠, A U_{3} = ⎛ ⎜ ⎝ \begin{matrix} 231 \end{matrix} ⎞ ⎟ ⎠

and

U

3 \times 3

matrix whose columns are

U_{1}, U_{2}

and

U_{3}

Then sum of the elements of

U^{- 1}

Q. Let the matrix

M = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 1 & 0 & 1 0 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦

satisfy

M^{n} = M^{n - 2} + M^{2} - I

for

n = 3, 4, 5, 6, \dots

where

I

is the identity matrix of order

3

.
Also

U_{1}, U_{2}, U_{3}

are column matrices satisfying

M^{50} U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 12525 \end{matrix} ⎤ ⎥ ⎦, M^{50} U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦, M^{50} U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦

and

U

is a

3 \times 3

matrix whose columns are

U_{1}, U_{2}, U_{3}

.
Then

Join BYJU'S Learning Program

A=⎡⎢⎣100210321⎤⎥⎦,U1,U2 and U3 are columns matrices satisfying AU1=⎡⎢⎣100⎤⎥⎦,AU2=⎡⎢⎣230⎤⎥⎦,AU3=⎡⎢⎣231⎤⎥⎦ and U is 3×3 matrix whose columns are U1,U2,U3 then answer the following questionThe sum of elements of U−1 is

The correct option is B 0U=⎡⎢⎣122−2−1−11−4−3⎤⎥⎦⇒|U|=−1−14+18=3Now, adjU=CT=⎡⎢⎣−1−79−2−560−33⎤⎥⎦T⇒adjU=⎡⎢⎣−1−20−7−5−3963⎤⎥⎦Hence, U−1=13⎡⎢⎣−1−20−7−5−3963⎤⎥⎦Now, sum of elements of U−1=0