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Statement-1:Determination of a skew-symm...

Statement-1:Determination of a skew-symmetric matrix of order 3 is zero.
Statement-2: For any matrix `det(A)^(T)=det(A)=-det(A)`.
Where det(B) denotes the determinant of matrix B. Then:

A

Statement I is true and Statement II is false

B

Both Statements are true

C

Both Statements are false

D

Statement I is false and Statement II is true

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The correct Answer is:
A
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Statement -1 : Determinant of a skew-symmetric matrix of order 3 is zero. Statement -2 : For any matrix A, Det (A) = "Det"(A^(T)) and "Det" (-A) = - "Det" (A) where Det (B) denotes the determinant of matrix B. Then,

If A is a skew-symmetric matrix of order 3, then prove that det A = 0 .

Assertion: Determinant of a skew symmetric matrix of order 3 is zero. Reason: For any matix A, det(A^T)=det(A) and det(-S)=-det(S) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true and R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If matric A is skew-symmetric matric of odd order, then show that tr. A = det. A.

If A is a matrix of order 3, then det(kA) is

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If one of the eigenvalues of a square matrix a order 3xx3 is zero, then prove that det A=0 .

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Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 If A is skew-symnmetric matrix of order 3, then its determinant should be zero. Statement - 2 If A is square matrix, det (A) = det (A') = det (-A')

If A is a skew symmetric matrix of order 3 , B is a 3xx1 column matrix and C=B^(T)AB , then which of the following is false?

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
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  2. If the trivial solution is the only solution of the system of equation...

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  3. Statement-1:Determination of a skew-symmetric matrix of order 3 is zer...

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  4. If omega=1 is the complex cube root of unity and matrix H=|{:(,omega,0...

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  5. Consider the system of linear equations: x(1) + 2x(2) + x(3) = 3 2...

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  6. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

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  7. Let a be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I ...

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  8. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

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  9. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  10. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity...

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  11. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  12. Let A be a square matrix all of whose entries are integers. Which on...

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  13. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  14. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  15. If A and B f are square matrices of size nxxn such that A^(2) - B^(2...

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  16. Let A =((1,2),(3,4))and B= ((a,0),(0,b)), a, bin N. Then,

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  17. If A is a square matrix such that A^2-A+l=0, then the inverse of A is

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  18. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  20. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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