Determinants questions
307 published questions with worked solutions.
- Consider the following in respect of a non-singular matrix M : I. |M^2|=|M|^2 II. |M|=|M^ -1 | III. |M|=|M^ T | How many of the...
- In obtaining the solution of the system of equations x+y+z=7, x+2y+3z=16 and x+3y+4z=22 by Cramer's rule, the value of y is...
- The value of the determinant vmatrix a&b&c &m&n &q&r vmatrix is equal to
- If a, b, c are the sides of a triangle ABC and p is the perimeter of the triangle, then what is vmatrix p+c&a&b &p+a&b &a&p+b...
- Consider the following statements : Statement-I : If X is an n n matrix, then (mX)=m^n (X), where m is a scalar. Statement-II :...
- If A is a square matrix such that |A|=-2, then |AA^T|, where A^T is the transpose of A, is equal to
- If M_k= bmatrix k&k-1 -1&k bmatrix where k is a natural number, then what is |M_1|+|M_2|+|M_3|+ +|M_ 50 | equal to?
- If M is a square matrix such that M^3=M, then how many values of |M| are possible?
- Let p=(x+y+z) and q=xyz. If vmatrix x&1&1 1&y&1 1&1&z vmatrix is positive, then which one of the following is correct?
- What is vmatrix 1 a &bc&a^3 1 a + 1 b &c(a+b)&a^3+b^3 1 a + 1 b + 1 c &ab+bc+ca&a^3+b^3+c^3 vmatrix equal to?
- If x+ay+a^2z=1, x+by+b^2z=1, x+cy+c^2z=1 where a b c, then what is x+y+z equal to?
- If is the value of the determinant vmatrix a_1 & b_1 & c_1 a_2 & b_2 & c_2 a_3 & b_3 & c_3 vmatrix then what is the value of the...
- If a+b+c=4 and ab+bc+ca=0, then what is the value of the following determinant? vmatrix a & b & c b & c & a c & a & b vmatrix
- If a_1, a_2, a_3, , a_9 are in GP, then what is the value of the following determinant? vmatrix a_1 & a_2 & a_3 a_4 & a_5 & a_6...
- Let A= vmatrix p & q r & s vmatrix where p, q, r and s are any four different prime numbers less than 20. What is the maximum...
- If A and B are square matrices of order 2 such that (AB)= (BA), then which one of the following is correct?
- If f(x)= vmatrix 1 & x & x+1 2x & x(x-1) & x(x+1) 3x(x-1) & 2(x-1)(x-2) & x(x+1)(x-1) vmatrix then what is f(-1)+f(0)+f(1) equal...
- The element in the ith row and the jth column of a determinant of third order is equal to 2(i+j). What is the value of the...
- With the numbers 2, 4, 6, 8, all the possible determinants with these four different elements are constructed. What is the sum of...
- If = vmatrix a & b & c d & e & f g & h & i vmatrix then what is vmatrix 3d+5g & 4a+7g & 6g 3e+5h & 4b+7h & 6h 3f+5i & 4c+7i & 6i...
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