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Standard XII

Mathematics

Diagonal Matrix

i. Trace of t...

Question

i. Trace of the matrix is called sum of the elements in a principle diagonal of the square matrix.
ii. The trace of the matrix $⎡ ⎢ ⎣ \begin{matrix} 8 & 7 & 5 5 & 8 & 2 7 & 2 & 8 \end{matrix} ⎤ ⎥ ⎦$ is 24 Which of the following statement is correct.

Only i

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Only ii

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Both i and ii

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Neither i nor ii

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Solution

The correct option is D Both i and ii
$(i) \to$ definition of matrix
$(i i)$ Sum of elements in principle diagonal
$= 8 + 8 + 8 = 24$
Option is correct

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Similar questions

Q. If trace of the square matrix

A = [a_{i j}]_{n \times n}

is zero, where

a_{i i} = i (i - 3),

then the order of the matrix is

Q. If

A

is a

3 \times 3

skew symmetric matrix with real entries and trace of

A^{2}

equals zero, then

Note: Trace of matrix

A

denotes the sum of diagonal elements of matrix

A

Q. Let

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

satisfies

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

for

n \geq 3.

And trace of a square matrix

X

is equal to the sum of elements in its principal diagonal. Further consider a matrix

\cup_{3 \times 3}

with its column as

\cup_{1}, \cup_{2}, \cup_{3}

such that

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

Then,

Trace of

A^{50}

equals

Q. If

A

be a non-singular matrix of order

2,

such that

∣ ∣ A + | A | adj (A) ∣ ∣ = 0,

then which of the following option(s) is/are always correct ?
(where

adj (A)

is the adjoint of matrix

A

)

Q. The trace of a square matrix is defined to be the sum of its diagonal entries. If

A

is a

2 \times 2

matrix such that the trace of

A

3

and the trace of

A^{3}

- 18,

then the value of the determinant of

A

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i. Trace of the matrix is called sum of the elements in a principle diagonal of the square matrix. ii. The trace of the matrix ⎡⎢⎣875582728⎤⎥⎦ is 24 Which of the following statement is correct.

The correct option is D Both i and ii(i)→definition of matrix(ii) Sum of elements in principle diagonal =8+8+8=24Option is correct

i. Trace of the matrix is called sum of the elements in a principle diagonal of the square matrix.
ii. The trace of the matrix $⎡ ⎢ ⎣ \begin{matrix} 8 & 7 & 5 5 & 8 & 2 7 & 2 & 8 \end{matrix} ⎤ ⎥ ⎦$ is 24 Which of the following statement is correct.

The correct option is D Both i and ii
$(i) \to$ definition of matrix
$(i i)$ Sum of elements in principle diagonal
$= 8 + 8 + 8 = 24$
Option is correct