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Mathematics Video Lectures

 
 

Notice BoardMaths Teaser of the Day

Q1-4(Elementary Matrices) : An elementary matrix is a matrix which is obtained by performing a single elementary row operation on the identity matrix. Recall the three kinds of elementary row operations we talked about -- (i) Interchanging two rows, (ii) Multiplying a row by a non-zero scalar, (iii) Adding a multiple of one row to another. Thus, the matrices A,B,C shown below are Elementary Matrices.

Matrix A is obtained by interchanging R1 and R2 of identity matrix, matrix B is obtained from identity matrix by multiplying R2 by r, matrix C is obtained by adding r times R2 to R3.

Let Eij denotes the elementary matrix obtained by interchanging i-th and j-th rows of identity matrix and Tij(r) denotes the elementary matrix obtained by adding r times i-th row to j-th row.

Q1. Which of the following is TRUE regarding matrices Eij  and Tij(r) :

Choose correct answer:
Eji = Eji
Eij2= I where I is an identity matrix
Tij(r) = Tji (r)
Tij(r).Tij(-r) = I where I is an identity matrix

 
 

Science Video Lectures

 
 

Notice BoardScience Teaser of the Day

A particle of mass m is attached to a spring of spring constant k, and has a natural angular velocity 0. An external force F(t) proportional to cos t is applied to the partical. The time displacement of the oscillator will be proportional to : 
Choose correct answer:
m/( 02 – 2 )
1/m( 02 – 2 )
1/m( 02 + 2 )
m/( 02 + 2 )

 
 
 
 

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    pithy, compact saying
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