Maths-
General
Easy

Question

A square matrix open square brackets a subscript i j end subscript close square brackets equals 0 for i space not equal to j and a subscript i j end subscript equals K (constant) for i equals j is called a

  1. unit matrix
  2. scalar matrix
  3. Null matrix
  4. Diagonal matrix

hintHint:

Matrix of size n in n cross times n square matrix with1 on the main diagonal and zero elsewhere is Unit matrix. A diagonal matrix is a matrix having non-zero elements only in the diagonal running from the upper left to the lower right. A scalar matrix is the special case diagonal matrix with all the diagonals elements equal and all off-diagonals element not equal. Null matrix is the matrix with all the elements zero.

The correct answer is: scalar matrix


    L e t space A equals open square brackets a subscript i j end subscript close square brackets space i s space a space s q u a r e space m a t r i x
a subscript i j end subscript equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 0 comma end cell cell i f space i not equal to j end cell row cell k comma end cell cell i f space i equals j end cell end table close
A equals open square brackets table row cell a subscript 11 end cell cell a subscript 12 end cell row cell a subscript 21 end cell cell a subscript 22 end cell end table close square brackets equals space open square brackets table row k 0 row 0 k end table close square brackets
T h u s comma space A space i s space s c a l a r space m a t r i x.

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