CameraIcon

SearchIcon

MyQuestionIcon

1

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

Addition and Subtraction of a Matrix

If Tr A =[2+ ...

Question

If Tr(A)=[2+i] then Tr[(2-i)A]=

(This lesson is from matrix not linear programming)

[The lesson matrix doesn't exist in chapter's list above pls refer and add matrix in chapter's list . ]

Open in App

Solution

(2-i)A means each element of matrix A is multiplied by (2-i)

Trace is the sum of main diagonal elements of a square matrix.

Tr(A)=2+i
Therefore
Tr(A(2-i) ) = (2-i)(2+i)
=4-i²
=4-(-1)
=5

Suggest Corrections

thumbs-up

3

Similar questions

Q. Sir/Ma'am,
I just wanted to get an explanation of the GAIA HYPOTHESIS given on-the-go above chapter's introduction (interaction and existence)..

Q. Observe the following lists :
List - I List - II
A) If A is a singular 1)

{(d e t A)}^{n - 1}

matrix then adj A is
B) If A is a square 2) an idempotent Matrix
matrix then detA=
C) If

A^{2}

=A then A is 3) Singular
D) If A is square matrix 4)

d e t A^{T}

of type n then det (adj A) = 5) a nil potent matrix
The correct match for list - I from list - II is

2 \times 2

matrix with non-zero entries and let

A^{2} = I

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

| A | = 1

\begin{matrix} L i s t I - ------- - & L i s t I I - -------- - 2 & 3 4 & 5 7 & 6 \end{matrix}

One number is to be selected at random from each of the lists above. What is the probability that both of the numbers selected will be less than

5

?

Q. Assertion :Let

A

2 \times 2

matrix with real entries. Let

I

2 \times 2

identity matrix. Denote by

t r (A)

, the sum of diagonal entries of

A

A^{2} = I

.

A \neq I

A \neq - I

d e t (A) = - 1

A \neq I

A \neq - I

t r (A) \neq 0

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebraic Operations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Addition and Subtraction of a Matrix

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon