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

Byju's Answer

Standard XII

Mathematics

Equality of Matrices

TrA+BT+3C equ...

Question

$T_{r} (A + B^{T} + 3 C)$ equals-
(where $T_{r} (A)$ denotes trace of matrix of $A$ )

17

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

18

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

20

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

21

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

Open in App

Solution

The correct option is A $17$
$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 1 & 1 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$
$B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 2 - 2 & - 1 & - 2 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦ B^{T} = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 2 & 2 2 & - 1 & 2 3 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦$
$C = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 2 & - 2 2 & 1 & 2 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦ 3 C = ⎡ ⎢ ⎣ \begin{matrix} - 3 & - 6 & - 6 6 & 3 & 6 6 & 6 & 9 \end{matrix} ⎤ ⎥ ⎦$
Trace $(A + B^{T} + 3 C)$
$= t r (A) + t r (B^{T}) + t r (3 C)$
$= (1 + 1 + 3) + (1 - 1 + 3) + (- 3 + 3 + 9)$
$= 5 + 3 + 9 = 17$
Option A

Suggest Corrections

Similar questions

Q. Consider three matrices

A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}] B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]

and

C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

.
The value of the sum

t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A ({B C)}^{2}}{4}) + t r (\frac{A ({B C)}^{3}}{8}) + . . . . . . . . . . . . . + \infty

is
(

t r (A)

denotes trace of a matrix

A

)

Q. Let three matrices

A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}]

;

B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]

and

C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

then find

t r (A) + t r (\frac{A B C}{2}) t r (\frac{A {(B C)}^{2}}{4}) + t r (\frac{A {(B C)}^{3}}{8}) + . . . . + \infty

, where

t r (A)

represents trace of matrix

A

Q. Let

A = ⎛ ⎜ ⎝ \begin{matrix} x^{2} & 6 & 8 3 & y^{2} & 9 4 & 5 & z^{2} \end{matrix} ⎞ ⎟ ⎠

and

B = ⎛ ⎜ ⎝ \begin{matrix} 2 x & 3 & 5 2 & 2 y & 6 1 & 4 & 2 z - 3 \end{matrix} ⎞ ⎟ ⎠

be two matrices and if

T r (A) = T r (B)

, then the value of

(x + y + z)

is equal to
(Note:

T r (P)

denotes trace of matrix

P

)

Q. If

λ = 3,

then

\frac{1}{7} (t r (A B) + t r (B A))

is equal to

Note:

t r (A)

denotes sum of diagonal elements of matrix

A

Q. Let A be a

2 \times 2

matrix with non-zero entries and let

A^{2} = I

, where I is

2 \times 2

identity matrix. Define Tr(A)

=

sum of diagonal elements of A and

| A | =

determinant of matrix A.
Statement-1 Tr(A)

= 0

Statement-2:

| A | = 1

Join BYJU'S Learning Program

Tr(A+BT+3C) equals-(where Tr(A) denotes trace of matrix of A)

The correct option is A 17A=⎡⎢⎣123211223⎤⎥⎦B=⎡⎢⎣122−2−1−2223⎤⎥⎦BT=⎡⎢⎣1−222−123−23⎤⎥⎦C=⎡⎢⎣−1−2−2212223⎤⎥⎦3C=⎡⎢⎣−3−6−6636669⎤⎥⎦Trace(A+BT+3C)=tr(A)+tr(BT)+tr(3C)=(1+1+3)+(1−1+3)+(−3+3+9)=5+3+9=17Option A

$T_{r} (A + B^{T} + 3 C)$ equals-
(where $T_{r} (A)$ denotes trace of matrix of $A$ )