Definition of a Determinant
Trending Questions
Q.
Does every matrix have a determinant?
Q. Determinant of a square matrix is a scalar quantity uniquely associated to that particular matrix.
- True
- False
Q. Let A be a 3×3 matrix such that det(A)=a=3 and B=adj(A) such that det(B)=b. Then the value of (3b2+9b+1)S, where 12S=ab+a2b3+a3b5+⋯ upto ∞, is
- 175
- 224
- 225
- 325
Q. The minimum value of (6+x)(11+x)(2+x), x≥0 is
- 45
- 25
- 5
- 15
Q. If the co-factor C21 (Cofactor of element of ith row &jth column) of the matrix ∣∣∣5200−1∣∣∣ is α and the value of the determinant is β, then β−α is
Q. Match List I with the List II and select the correct answer using the code given below the lists :
List IList II(A) If →a=t^i−3^j+2t^k, →b=^i−2^j+2^k and →c=3^i+t^j−^k, then the(P)1value of ⎛⎜⎝2∫1→a⋅(→b×→c)dt+2⎞⎟⎠ is equal to(B)The value of t∈R for which the vectors →a=(1, −2, 3), →b=(−2, 3, −4), (Q)2→c=(1, −1, t) form a linearly dependent system is(C)If the area of the parallelogram whose diagonals are 3^i+^j−2^k and(R)3^i−3^j+4^k is μ√3 sq. unit, then the value of μ is(D)Let →p=^i+^j, →q=^i−^j and →r=^i+2^j+3^k. If →x is a unit vector(S)4such that →p⋅→x=0 and →q⋅→x=0, then |→r⋅→x| is equal to(T)5
Which of the following is the only CORRECT combination ?
List IList II(A) If →a=t^i−3^j+2t^k, →b=^i−2^j+2^k and →c=3^i+t^j−^k, then the(P)1value of ⎛⎜⎝2∫1→a⋅(→b×→c)dt+2⎞⎟⎠ is equal to(B)The value of t∈R for which the vectors →a=(1, −2, 3), →b=(−2, 3, −4), (Q)2→c=(1, −1, t) form a linearly dependent system is(C)If the area of the parallelogram whose diagonals are 3^i+^j−2^k and(R)3^i−3^j+4^k is μ√3 sq. unit, then the value of μ is(D)Let →p=^i+^j, →q=^i−^j and →r=^i+2^j+3^k. If →x is a unit vector(S)4such that →p⋅→x=0 and →q⋅→x=0, then |→r⋅→x| is equal to(T)5
Which of the following is the only CORRECT combination ?
- (C)→(Q), (D)→(P)
- (C)→(T), (D)→(R)
- (C)→(R), (D)→(P)
- (C)→(Q), (D)→(R)
