हिंदी

By using properties of determinants, prove that |x+yy+zz+xzxy111| = 0.

Advertisements
Advertisements

प्रश्न

By using properties of determinants, prove that `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|` = 0.

योग
Advertisements

उत्तर

L.H.S. = `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|` 

Applying R1 → R1 + R2, we get

L.H.S. = `|(x + y + z, x + y + z, x + y + z),(z, x , y),(1, 1, 1)|`

Taking (x + y + z) common from R1, we get

L.H.S. = `(x + y + z)|(1, 1, 1),(z, x, y),(1, 1, 1)|`

= (x + y + z) (0)          …[∵ R1 and R3 are identical]
= 0
= R.H.S.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Determinants - MISCELLANEOUS EXERCISE - 6 [पृष्ठ ९५]

APPEARS IN

बालभारती Mathematics and Statistics (Commerce) Part 1 [English] Standard 11 Maharashtra State Board
अध्याय 6 Determinants
MISCELLANEOUS EXERCISE - 6 | Q 3) | पृष्ठ ९५

संबंधित प्रश्न

Using properties of determinants, prove that

`|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3`

 


 

Using properties of determinants, prove that 

`|[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|`

 

By using properties of determinants, show that:

`|(1,1,1),(a,b,c),(a^3, b^3,c^3)|` = (a-b)(b-c)(c-a)(a+b+c)


By using properties of determinants, show that:

`|(1,x,x^2),(x^2,1,x),(x,x^2,1)| = (1-x^3)^2`


Using properties of determinants, prove that 

`|(a^2 + 2a,2a + 1,1),(2a+1,a+2, 1),(3, 3, 1)| = (a - 1)^3`


Evaluate the following determinants:

`|(x - 1, x, x - 2),(0, x - 2, x - 3),(0, 0, x - 3)| = 0`


Without expanding determinants, prove that `|(1, yz, y + z),(1, zx, z + x),(1, xy, x + y)| = |(1, x, x^2),(1, y, y^2),(1, z, z^2)|`.


Without expanding the determinants, show that `|(x"a", y"b", z"c"),("a"^2, "b"^2, "c"^2),(1, 1, 1)| = |(x, y, z),("a", "b", "c"),("bc", "ca", "ab")|`


Using properties of determinant show that

`|("a" + "b", "a", "b"),("a", "a" + "c", "c"),("b", "c", "b" + "c")|` = 4abc


Using properties of determinant show that

`|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` = 0


Select the correct option from the given alternatives:

If x = –9 is a root of `|(x, 3, 7),(2, x, 2),(7, 6, x)|` = 0 has other two roots are


Evaluate: `|(x^2 - x + 1, x - 1),(x + 1, x + 1)|`


The number of distinct real roots of `|(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx, cosx, sinx)|` = 0 in the interval `pi/4  x ≤ pi/4` is ______.


If cos2θ = 0, then `|(0, costheta, sin theta),(cos theta, sin theta,0),(sin theta, 0, cos theta)|^2` = ______.


Let P be any non-empty set containing p elements. Then, what is the number of relations on P?


If `|(α, 3, 4),(1, 2, 1),(1, 4, 1)|` = 0, then the value of α is ______.


The value of the determinant `|(6, 0, -1),(2, 1, 4),(1, 1, 3)|` is ______.


Without expanding determinants find the value of `|(10,57,107), (12, 64, 124), (15, 78, 153)|`


Without expanding determinants find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`


By using properties of determinants, prove that 

`|(x+y, y+z, z+x),(z, x, y),(1, 1, 1)|` = 0 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×