English

If α|α34121141| = 0, then the value of α is ______. - Mathematics

Advertisements
Advertisements

Question

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

Options

  • 1

  • 2

  • 3

  • 4

MCQ
Fill in the Blanks
Advertisements

Solution

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

Explanation:

If two rows/columns are identical in any determinant, the value becomes zero.

In given determinant on comparing C1 and C3.

We conclude α = 4.

shaalaa.com
  Is there an error in this question or solution?
2022-2023 (March) Delhi Set 1

RELATED QUESTIONS

Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z,z-x-y],[x-y-z,2x,2x]|=(x+y+z)^3`


Using the properties of determinants, prove the following:

`|[1,x,x+1],[2x,x(x-1),x(x+1)],[3x(1-x),x(x-1)(x-2),x(x+1)(x-1)]|=6x^2(1-x^2)`


By using properties of determinants, show that:

`|(x+4,2x,2x),(2x,x+4,2x),(2x , 2x, x+4)| = (5x + 4)(4-x)^2`


Using properties of determinants show that

`[[1,1,1+x],[1,1+y,1],[1+z,1,1]] = xyz+ yz +zx+xy.`


Using properties of determinants, prove that \[\begin{vmatrix}a + x & y & z \\ x & a + y & z \\ x & y & a + z\end{vmatrix} = a^2 \left( a + x + y + z \right)\] .


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 determinant, find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`.


Without expanding the determinants, show that `|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")| = |("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`


Prove that `|(x + y, y + z, z + x),(z + x, x + y, y + z),(y + z, z + x, x + y)| = 2|(x, y, z),(z, x, y),(y, z, x)|`


Without expanding determinants show that

`|(1, 3, 6),(6, 1, 4),(3, 7, 12)| + 4|(2, 3, 3),(2, 1, 2),(1, 7, 6)| = 10|(1, 2, 1),(3, 1, 7),(3, 2, 6)|`


Select the correct option from the given alternatives:

The determinant D = `|("a", "b", "a" + "b"),("b", "c", "b" + "c"),("a" + "b", "b" + "c", 0)|` = 0 if


Answer the following question:

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


Answer the following question:

Without expanding determinant 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")|`


Answer the following question:

If `|("a", 1, 1),(1, "b", 1),(1, 1, "c")|` = 0 then show that `1/(1 - "a") + 1/(1 - "b") + 1/(1 - "c")` = 1


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


Evaluate: `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`


Evaluate: `|(3x, -x + y, -x + z),(x - y, 3y, z - y),(x - z, y - z, 3z)|`


The value of the determinant `|(x , x + y, x + 2y),(x + 2y, x, x + y),(x + y, x + 2y, x)|` is ______.


If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.


Let Δ = `|("a", "p", x),("b", "q", y),("c", "r", z)|` = 16, then Δ1 = `|("p" + x, "a" + x, "a" + "p"),("q" + y, "b" + y, "b" + "q"),("r" + z, "c" + z, "c" + "r")|` = 32.


A system of linear equations represented in matrix form Ax = 0, A is n × n matrix, has a non-zero solution if the determinant of A (i.e., det(A)) is


`f : {1, 2, 3) -> {4, 5}` is not a function, if it is defined by which of the following?


If f(α) = `[(cosα, -sinα, 0),(sinα, cosα, 0),(0, 0, 1)]`, prove that f(α) . f(– β) = f(α – β).


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


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


The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of the determinant of C2?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×