Maths-
General
Easy
Question
Set of equations
and
is consistent for
equal to
- 1
- 0
- –1
- 2
The correct answer is: 0
![a plus b minus 2 c equals 0](data:image/png;base64,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)
![2 a minus 3 b plus c equals 0](data:image/png;base64,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)
![a minus 5 b plus 4 c equals alpha](data:image/png;base64,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)
System is consistent, if
=0
and
= 0 and
also zero.
Hence, value of
is zero.
Related Questions to study
Maths-
The number of solutions of the equations
is
The number of solutions of the equations
is
Maths-General
Maths-
Maths-General
Maths-
If
, then x =
If
, then x =
Maths-General
Maths-
Maths-General
Maths-
If
are three consecutive positive integers, then ![fraction numerator 1 over denominator 2 end fraction log subscript e end subscript invisible function application x plus fraction numerator 1 over denominator 2 end fraction log subscript e end subscript invisible function application z plus fraction numerator 1 over denominator 2 x z plus 1 end fraction plus fraction numerator 1 over denominator 3 end fraction open parentheses fraction numerator 1 over denominator 2 x z plus 1 end fraction close parentheses to the power of 3 end exponent plus.... equals](data:image/png;base64,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)
If
are three consecutive positive integers, then ![fraction numerator 1 over denominator 2 end fraction log subscript e end subscript invisible function application x plus fraction numerator 1 over denominator 2 end fraction log subscript e end subscript invisible function application z plus fraction numerator 1 over denominator 2 x z plus 1 end fraction plus fraction numerator 1 over denominator 3 end fraction open parentheses fraction numerator 1 over denominator 2 x z plus 1 end fraction close parentheses to the power of 3 end exponent plus.... equals](data:image/png;base64,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)
Maths-General
Maths-
The value of
is
The value of
is
Maths-General
Maths-
The sum of the products of the elements of any row of a determinant A with the same row is always equal to
The sum of the products of the elements of any row of a determinant A with the same row is always equal to
Maths-General
Maths-
is divisor of
is divisor of
Maths-General
Maths-
If
,then the value of k is
If
,then the value of k is
Maths-General
Maths-
The value of the determinant
is
The value of the determinant
is
Maths-General
Maths-
If
the value of t is
If
the value of t is
Maths-General
Maths-
If
are unequal what is the condition that the value of the following determinant is zero ![capital delta equals open vertical bar table row a cell a to the power of 2 end exponent end cell cell a to the power of 3 end exponent plus 1 end cell row b cell b to the power of 2 end exponent end cell cell b to the power of 3 end exponent plus 1 end cell row c cell c to the power of 2 end exponent end cell cell c to the power of 3 end exponent plus 1 end cell end table close vertical bar](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIcAAABHCAYAAAAtD1S+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAo9ZE6ZAAABEhJREFUeNrtnT9oFEEUxocQQooghJBCRAQJIpJOJIiIjViIiK2FiAgWVhIEkSNICAGxsBAbsRAREYIECwk2EoKITZBgJYKFhcgREBGREIT1DfuCy7q3uzPzdnbu5vvgFXfI++Zmfzt/1n0ZpaAdJRzbFG8ppjx5bVCcQvf/30EhaojiKsV7T34HKb7g2vQHHDva8gjjd8DRP3CcoFjz4DNBcZ/iUoMeByjmePoCHI7azWuO/Z7WOBca9nlCccWwvwFHj7vsJQPiQ7soFvniNd1vAwWHnovnKbqZVf0+h3m9KpcGYoUvmOsawrTdW4DDrAH6Dr5HMc4dvkRxztKrTq4V3jm4yrTdxynWAUf9BpznTs3qMcVpC5+6uZKCaNpLjxivDEfE6OFYpTia+27NclqRzNWGV1IjooLjNw/J2Xn8l6WPZK4QvKIfOTZzn48p+yeWkrlC8Ioejq8Uo5nP+iHOc0sfyVwheEUPxwLFAx6W9Xz9lHcTNpLMFYIXtrKkDq/85/hu7DpsZSVzheRlu6DtezjymhT0nvT4OydV/wmPzyHAAQEOCHBAgAMCHBDgAByAA3AADsABOAAH4AAcuTah6g1wlCr2qrekTge9jnxaibXqrfLa3OIhbyZSOAap6k302kxTvGNAFlqEI/9OpotMcrlWvdX18lX1ZloSmZQNceuc8DDFh5bgmBL0NsnlWvVm2m6bqjdTmZZE9vx3mrCbmc/fKlbttq/OVzVUvz31TKhz6uaSqHqzbXdIVW9Jr+kkX331kGK2hZFDT2n6lbt5BlR33qrlHV03l0TVm027Q6t6S3pNJ4dy359taGFW1VD9HuZnihvqX2nhXcu7sm4uiao3U68Qq96SoumkU/APh/kHTHieVj4VgKqH+58WnSKZKwQvr3BMVwxrLyguehw5hnjFn9eoRSdL5mrLy3dJZFI1nWSlV7o+i3NmeJ7OS9ehmj6Yk8wVipe3kaPDU0rVKn6bpxgfP1BXqz8q+H62RlubzBWKlzc4ftQctnSMePqB+u9b5J8YjvDzA9PdimSuULxa2cr6VFkDlnlhd5I/7+HvbB4xS+YKxStqOLq8hdYd/Uelj31tSwolc4Xk5bqg7Vs4oMivDeAAHIADcAAOwAE4AAfgAByAAwIcEOCAAAcEOCDAEVKHoBQScJQKBwACjkrhAEDAUaiYSyEBR4kG7QBAnA4p2JGhHwBoKpwOKTRiSBwA2PT6BqcmZDRGcUelZ5norZ9+J3Pc0rMsl9QBgKbtxgGAlg0Y4y3lIt/R+k3u6xRnLC9WWS6JUkhTLxwA6NCA2yp93V9Ckrna9AIcvP/fdJhCmsrl2wunQxboCMUbIS/JXG17YeRQ6UG9y0Jekrna9gIcKv2TUx+FvCRzte0FOFgbvOIf5lX/NZWe1WojyVxtegEO1l6V/h+HLi3UxciXHfwkc4XkZbOgHQg4oEivDeAIHI6/8vxDE6Y0ZW4AAAJDdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDM5NDs8L21pPjxtbz49PC9tbz48bWZlbmNlZCBjbG9zZT0ifCIgb3Blbj0ifCIgc2VwYXJhdG9ycz0ifCI+PG10YWJsZT48bXRyPjxtdGQ+PG1pPmE8L21pPjwvbXRkPjxtdGQ+PG1zdXA+PG1pPmE8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tdGQ+PG10ZD48bXN1cD48bWk+YTwvbWk+PG1uPjM8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bWk+YjwvbWk+PC9tdGQ+PG10ZD48bXN1cD48bWk+YjwvbWk+PG1uPjI8L21uPjwvbXN1cD48L210ZD48bXRkPjxtc3VwPjxtaT5iPC9taT48bW4+MzwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bW4+MTwvbW4+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtaT5jPC9taT48L210ZD48bXRkPjxtc3VwPjxtaT5jPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXRkPjxtdGQ+PG1zdXA+PG1pPmM8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj4xPC9tbj48L210ZD48L210cj48L210YWJsZT48L21mZW5jZWQ+PC9tYXRoPmLjWokAAAAASUVORK5CYII=)
If
are unequal what is the condition that the value of the following determinant is zero ![capital delta equals open vertical bar table row a cell a to the power of 2 end exponent end cell cell a to the power of 3 end exponent plus 1 end cell row b cell b to the power of 2 end exponent end cell cell b to the power of 3 end exponent plus 1 end cell row c cell c to the power of 2 end exponent end cell cell c to the power of 3 end exponent plus 1 end cell end table close vertical bar](data:image/png;base64,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)
Maths-General
Maths-
If – 9 is a root of the equation
then the other two roots are
If – 9 is a root of the equation
then the other two roots are
Maths-General
Maths-
If
is a cube root of unity, then ![open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals](data:image/png;base64,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)
If
is a cube root of unity, then ![open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General