There are 4 routes from city A to city B, 5 routes from city B to city C and 3 routes from city C to city A. Convert the above information into matrix form.
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A square matrix `P` satisfies `P^(2)=I-P` where `I` is identity matrix. If `P^(n)=5I-8P`, then `n` is
Correct Answer - C `(c )` `P^(3)=P(I-P)=P-P^(2)=P-(I-P)=2P-1` `P^(4)=P(2P-I)=2(I-P)-P=2I-3P` `P^(5)=P(2I-3P)=2P-3(IP)=5P-3I` `P^(6)=P(5P-3I)=5(I-P)-3P=5I-8P` So `n=6`
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If matrix `A=[a_(ij)]_(3xx)`, matrix `B=[b_(ij)]_(3xx3)`, where `a_(ij)+a_(ji)=0` and `b_(ij)-b_(ji)=0 AA i`, `j`, then `A^(4)*B^(3)` is
Correct Answer - A `(a)` Here `a_(ij)+a_(ji)=0impliesA^(T)=-A` and `b_(ij)-b_(ji)=0impliesB^(T)=B` and `A,B` are `3xx3` matrices, Hence `|A|=0`, `implies|A^(4)B^(3)|=0` gtbrgt `impliesA^(4)B^(3)` is singular matrix.
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Let `A` be a square matrix of order `3` so that sum of elements of each row is `1`. Then the sum elements of matrix `A^(2)` is
Correct Answer - B `(b)` Let `A=[{:(a,b,c),(p,q,r),(x,y,z):}]` Given `{:(a+b+c=1),(p+q+r=1),(x+y+z=1):}` `impliesA^(2)=[{:(a,b,c),(p,q,r),(x,y,z):}][{:(a,b,c),(p,q,r),(x,y,z):}]` `=[{:(a^(2)+bp+cx,,ab+bq+cy,,ac+br+cz),(pa+qp+rx,,qb+q^(2)+ry,,pc+qr+rz),(xa+yp+zx,,xb+yq+zy,,xc+yr+z^(2)):}]` Sum of elements of `R_(1)=a^(2)+bp+cx+ab+bq+cy+ac+br+cz` `=a(a+b+c)+b(p+q+r)+c(x+y+z)` `=a+b+c=0` Similarly sum of elements of `R_(2)=p(a+b+c)+q(p+q+r)+r(x+y+z)` `=p+q+r=1` `R_(3)=x(a+b+c)+y(p+q+r)+z(x+y+z)` `=x+y+z=1` `:.` sum of element...
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A be a square matrix of order `2` with `|A| ne 0` such that `|A+|A|adj(A)|=0`, where `adj(A)` is a adjoint of matrix `A`, then the value of `|A-|A|adj
Correct Answer - D `(d)` Let `A=[{:(m,n),(p,q):}]`,`adj(a)=[{:(q,-n),(-p,m):}]` Let `|A|=d=mq-np` `|A+dadjA|=|{:(m+qd,n(1-d)),(p(1-d),q+md):}|=0` `impliesmq+m^(2)d+q^(2)d+mqd^(2)-np+2npd-npd^(2)=0` `implies(mq-np)+(mq0np)d^(2)+m^(2)d+q^(2)d+2mqd-2d^(2)=0` `implies(d+d^(3)-2d^(2))+d(m^(2)+q^(2)+2mq)=0` Now, `|A- d adj|A|=-(m+q)^(2)+4(mq-np)=4d=4`
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If `A` is a skew symmetric matrix, then `B=(I-A)(I+A)^(-1)` is (where `I` is an identity matrix of same order as of `A`)
Correct Answer - C `(c )` `B=(I-A)(I+A)^(-1)` `impliesB^(T)=(I+A^(T))^(-1)(I-A^(T))` `=(I-A)^(-1)(I+A)` `impliesB B^(T)=(I-A)(I+A)^(-1)(I-A)^(-1)(I+A)` `=(I-A)(I-A)^(-1)(I+A)^(-1)(I+A)` `=I` (As `(I-A).(I+A)=(I+A)(I-A)`)
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If `A` is an idempotent matrix satisfying `(I-0.4A)^(-1)=I-alphaA` where `I` is the unit matrix of the same order as that of `A` then the value of `al
Correct Answer - C `(c )` Given `A^(2)=A` `impliesI=(I-0.4A)(I-alphaA)` `=I-IalphaA-0.4AI+0.4alphaA^(2)` `=I-Aalpha-0.4A+0.4alphaA` `=I-A(0.4+alpha)+0.4alphaA` `implies 0.4alpha=0.4+alpha` `impliesalpha=-(3)/(2)`
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Convert the above letter into an e-mail format.
To: [email protected] Cc: [email protected] Bcc: (non-visible email ids) Subject: Permission for organising mountaineering expedition Respected Sir/Madam, This is Harshad Kale, the representative of XYZ college of Arts and Commerce. On behalf of my teachers and...
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There is a milliameter, each division of which reads 1 mA. It has a resistance of `15Omega`. How would you convert it into a voltmeter, each division
Correct Answer - `958 Omega` in series
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Basing on the above information, which country has more equitable distribution and income?
Correct option is A) Country A
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The trade routes between the West and East were closed with which city fell into the hands of the Turks in 1453?
B) Constantinople
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