Advertisements
Advertisements
प्रश्न
Without expanding the determinant, find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`.
Advertisements
उत्तर
Let D = `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`
Applying C3 → C3 – C2, we get
D = `|(10, 57, 50),(12, 64, 60),(15, 78, 75)|`
Taking (5) common from C3, we get
D = `5|(10, 57, 10),(12, 64, 12),(15, 78, 15)|`
= 5(0) ...[∵ C1 and C3 are identical]
= 0
APPEARS IN
संबंधित प्रश्न
Using properties of determinants prove the following: `|[1,x,x^2],[x^2,1,x],[x,x^2,1]|=(1-x^3)^2`
Using the property of determinants and without expanding, prove that:
`|(2,7,65),(3,8,75),(5,9,86)| = 0`
By using properties of determinants, show that:
`|(0,a, -b),(-a,0, -c),(b, c,0)| = 0`
Without expanding the determinant, prove that
`|(a, a^2,bc),(b,b^2, ca),(c, c^2,ab)| = |(1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3)|`
Solve the following equation: `|(x + 2, x + 6, x - 1),(x + 6, x - 1,x + 2),(x - 1, x + 2, x + 6)|` = 0
Without expanding determinants, show that
`|(1, 3, 6),(6, 1, 4),(3, 7, 12)| + |(2, 3, 3),(2, 1, 2),(1, 7, 6)| = 10|(1, 2, 1),(3, 1, 7),(3, 2, 6)|`
Without expanding the determinants, show that `|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")| = |("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`
Using properties of determinant show that
`|("a" + "b", "a", "b"),("a", "a" + "c", "c"),("b", "c", "b" + "c")|` = 4abc
Answer the following question:
Without expanding determinant show that
`|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")| = |("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`
The value of determinant `|("a" - "b", "b" + "c", "a"),("b" - "a", "c" + "a", "b"),("c" - "a", "a" + "b", "c")|` is ______.
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 the ratio of the H.M. and GM. between two numbers a and bis 4 : 5, then a: b is
`f : {1, 2, 3) -> {4, 5}` is not a function, if it is defined by which of the following?
Which of the following is correct?
In a triangle the length of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be ______.
Without expanding evaluate the following determinant.
`|(1, a, a + c),(1, b, c + a),(1, c, a + b)|`
Without expanding determinant find the value of `|(10,57,107),(12,64,124),(15,78,153)|`
Without expanding evaluate the following determinant.
`|(1,"a","b+c"),(1,"b","c+a"),(1,"c","a+b")|`
Without expanding evaluate the following determinant.
`|(1, a, b+c), (1, b, c+a), (1, c, a+b)|`
