Determinants questions
307 published questions with worked solutions.
- If B is a non-singular matrix and A is a square matrix, then the value of (B^ -1 AB) is equal to
- If a b c, then one value of x which satisfies the equation vmatrix 0&x-a&x-b +a&0&x-c +b&x+c&0 vmatrix =0 is given by
- If vmatrix x&y&0 0&x&y &0&x vmatrix =0, then which one of the following is correct?
- The value of the determinant vmatrix ^2 2 & ^2 2 ^2 2 & ^2 2 vmatrix for all values of , is
- The system of equations kx+y+z=1, x+ky+z=k and x+y+kz=k^2 has no solution if k equals
- The value of the determinant vmatrix 1- & - ^2& ^2 1- & - ^2& ^2 1- & - ^2& ^2 vmatrix is equal to
- If p+q+r=a+b+c=0, then the determinant vmatrix pa&qb&rc &ra&pb &pc&qa vmatrix equals
- Which one of the following factors does the expansion of the determinant vmatrix x&y&3 ^2&5y^3&9 ^3&10y^5&27 vmatrix contain?
- If a+b+c=0, then one of the solutions of vmatrix a-x&c&b &b-x&a &a&c-x vmatrix =0 is
- The system of equations 2x+y-3z=5, 3x-2y+2z=5 and 5x-3y-z=16
- What is the determinant of the matrix pmatrix x&y&y+z &x&z+x &z&x+y pmatrix ?
- If A, B and C are the angles of a triangle and vmatrix 1&1&1 1+ A&1+ B&1+ C A+ ^2A& B+ ^2B& C+ ^2C vmatrix =0, then which one of...
- What is the value of the determinant vmatrix 1!&2!&3! 2!&3!&4! 3!&4!&5! vmatrix ?
- What are the values of x that satisfy the equation vmatrix x&0&2 2x&2&1 1&1&1 vmatrix + vmatrix 3x&0&2 ^2&2&1 0&1&1 vmatrix =0?
- If x+a+b+c=0, then what is the value of vmatrix x+a&b&c &x+b&c &b&x+c vmatrix ?
- For how many values of k, is the matrix bmatrix 0&k&4 -k&0&-5 -k&k&-1 bmatrix singular?
- Let A= bmatrix x+y&y 2x&x-y bmatrix , B= bmatrix 2 -1 bmatrix and C= bmatrix 3 2 bmatrix . If AB=C, then what is the value of the...
- What is the value of the determinant vmatrix i&i^2&i^3 ^4&i^6&i^8 ^9&i^ 12 &i^ 15 vmatrix where i= -1 ?
- Let p, q and r be three distinct positive real numbers. If D= vmatrix p&q&r &r&p &p&q vmatrix , then which one of the following...
- If _1= vmatrix 1&p&q 1&q&r 1&r&p vmatrix and _2= vmatrix 1&1&1 &r&p &p&q vmatrix where p q r, then _1+ _2 is
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