हिंदी

If A = [1242] then show that |2A| = 4|A| - Mathematics

Advertisements
Advertisements

प्रश्न

If A = `[(1,2),(4,2)]` then show that |2A| = 4|A|

योग

उत्तर

A = `[(1,2),(4,2)]`

=>` 2"A" = [(2,4),(8,4)]`

∴ |A| = `|(1,2),(4,2)|`

= 2 - 8

= - 6      ....(1)

|2A| = `|(2,4),(8,4)|`

= 2 × 4 - 4 × 8

= 8 - 32

= - 24      ...(2)

From equations (1) and (2),

|2A| = 4|A|

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Determinants - Exercise 4.1 [पृष्ठ १०८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 4 Determinants
Exercise 4.1 | Q 3 | पृष्ठ १०८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If ` x in N and |[x+3,-2],[-3x,2x]|=8` , then find the value of x.


Evaluate the determinant.

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


If A=`[(1,0,1),(0,1,2),(0,0,4)]` then show that `|3A| = 27|A|`


Evaluate the determinant.

`|(3,-4,5),(1,1,-2),(2,3,1)|`


Evaluate the determinant.

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


Evaluate the determinant.

`|(2,-1,-2),(0,2,-1),(3,-5,0)|`


If `|(x, 2),(18, x)| = |(6,2),(18,6)|`, then x is equal to ______.


Prove that the determinant `|(x,sin theta, cos theta),(-sin theta, -x, 1),(cos theta, 1, x)|` is independent of θ.


Evaluate `|(cos alpha cos beta, cos alpha sin beta, -sin alpha),(-sin beta, cos beta, 0),(sin alpha cos beta, sin alpha sin beta,cos alpha )|`


If ab and are real numbers, and triangle =`|(b+c, c+a, a+b),(c+a,a+b, b+c),(a+b, b+c, c+a)|` = 0 Show that either a + b + c = 0 or a = b = c.


Solve the equations `|(x+a,x,x),(a,x+a,x),(x,x,x+a)| = 0, a != 0`


Prove that `|(a^2, bc, ac+c^2),(a^2+ab, b^2, ac),(ab, b^2+bc, c^2)| = 4a^2b^2c^2`


In question 18, write the value of a11 C21 + a12 C22 + a13 C23.


If A is a square matrix satisfying AT A = I, write the value of |A|.


A is a skew-symmetric of order 3, write the value of |A|.


One root of the equation `abs ((3"x" - 8, 3,3),(3, 3"x" - 8, 3),(3,3,3"x" - 8)) = 0` is ____________.


If A `= [(2,3),(3,4)],` then find A-1.


Find a 2 x 2 matrix B such that B `= [(1, -2),(1,4)] = [(6,0),(0,6)]`


Let A = `((cos^2x, sin^2x),(sin^2x, cos^2x))` and B = `((sin^2x, cos^2x),(cos^2x, sin^2x))`. Then the determinant of the matrix A + B is


Evaluate `|(x, x + 1),(x - 1, x)|`


There are two number 'x' making the value of the `|(1, -2, 5),(2, x, -1),(0, 4, 2x)|` equals to 86. The sum of there two number, is:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×