Related InterviewSolutions

• If `A = [[1,2],[3,-5]]` and `B=[[1,0],[0,2]]` and X is a matrix such that `A=BX`, then X=A. `(1)/(2)[{:(,2,4),(,4,5):}]`B. `(1)/(2)[{:(,-2,4),(,3,5):}]`C. `[{:(,2,4),(,3,-5):}]`D. none of these
• If `|(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2` then the ordered pair (A,B) is equal toA. `(-4,5)`B. `(4,5)`C. `(-4,-5)`D. `(-4,3)`
• Let `A=|{:(,-2,7,sqrt3),(,0,0,-2),(,0,2,0):}| and A^(4)=lambda,I,"then"lambda "is"`A. `-16`B. 16C. 8D. `-8`
• Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of the set of all determinants with value `-1`. ThenA. Statement-1is true, Statement-2 is true and Statement-2 is correct explantion for Statement-1.B. Statement-1 is true, Statement-2 is true and Statement-2 is not correct explantion for Statement-1.C. Statement-1 is true, Statement-2 is false.D. Statement-1 is false, Statement-2 is false.
• Obtain the inverse of the matrix `A=[{:(2,3),(1,1):}]` using elementary operations.
• How many 3 x 3 skew symmetric matrices can be formed using numbers -2,-1,1,2,3,4. 0 (any num can be used any number of times but O can be used at most 3 times)A. 8B. 27C. 64D. 54
• Which of the following is true for matrox `A=[{:(,1,-1),(,2,3):}]`A. `A+4I` is a symmetric matrixB. `A^(2)-4A+5I_(2)=0`C. A-B is a diagonal matrix for any value of `alpha "if" =[{:(,alpha,-1),(,2,5):}]`D. A-4I is a skew symmetric matrix.
• If `a , b , c`are non-zero, then the system of equations`(alpha+a)x+alphay+alphaz=0,alphax+(alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0`has a non-trivial solution if`alpha^(-1)=-(a^(-1)+b^(-1)+c^(-1))`b. `alpha^(-1)=a+b+c`c.`alpha+a+b+c=1`d. none of theseA. `alpha^(-1)=-(a^(-1)+b^(-1)+c^(-1))`B. `alpha^(-1)=a+b+c`C. `alpha+a+b+c=1`D. none of these
• Let AX=B where A is `3 xx 3` and X and B are `3 xx 1` matrices then which of the following is correct?A. If |A|=0 then AX=B has infinite solutionsB. If AX=B has infinite solutions then |A|=0C. If (adj (A))B=0 `|A|ne0` then AX=B has unique solutionsD. If (adj (A))Bne0 `|A|ne0` then AX=B has no solution
• Let zt be the set of all `3 xx 3` summetric matrices whose entries are `1,1,1,0,0,0,-1,-1,`.B is one of the matrix in set zt and `X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}]` ltBRgt Number of matrices B in set is `lambda, "then" lamda` lies in the intervalA. (30,40)B. (38,40)C. (34,38)D. (25,35)