Reduce the matrix A(given below) to normal form and hence find its rank.

Asked by rahulksinha200 | 16th Oct, 2021, 02:08: PM

Expert Answer:

To check the cotinuity of the function:
straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator open vertical bar straight x close vertical bar over denominator straight x end fraction comma space space space straight x not equal to 0 end cell row cell 0 comma space space space space space space straight x equals 0 end cell end table close
space space space space space space equals open curly brackets table attributes columnalign left end attributes row cell straight x over straight x comma space space space straight x greater than 0 end cell row cell fraction numerator negative straight x over denominator straight x end fraction comma space space straight x less than 0 end cell row cell 0 comma space space space space space space straight x equals 0 end cell end table close
space space space space space space equals open curly brackets table attributes columnalign left end attributes row cell 1 comma space space space space space straight x greater than 0 end cell row cell negative 1 comma space space straight x less than 0 end cell row cell 0 comma space space space space straight x equals 0 end cell end table close
LHL equals limit as straight x rightwards arrow 0 to the power of minus of straight f open parentheses straight x close parentheses equals limit as straight x rightwards arrow 0 of open parentheses negative 1 close parentheses equals negative 1
RHL equals limit as straight x rightwards arrow 0 to the power of plus of straight f open parentheses straight x close parentheses equals limit as straight x rightwards arrow 0 of 1 equals 1
As space LHL not equal to RHL
So comma space straight f space is space not space continuous space at space straight x equals 0.

Answered by Renu Varma | 19th Oct, 2021, 12:12: PM

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