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The rank of a 3 x 3 matrix C (= AB), found by multiplying a nonzero column matrix A of size 3 x 1 and a nonzero row matrix B of size 1 x 3, is
In questions 1.1 to 1.7 below, one or more of the alternatives are correct. Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book. Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up. 1.1). The eigen vector (s) of the matrix
is (are)
Consider the following matrix
If the eigenvalues of A are 4 and 8, then
Consider the following determinant
Which of the following is a factor of Δ?
Let A be a matrix such that A^{k} = 0. What is the inverse of I  A?
F is an n*n real matrix. b is an n*1 real vector. Suppose there are two n*1 vectors, u and v such that, u ≠ v and Fu = b, Fv = b. Which one of the following statements is false?
Perform the following operations on the matrix
i. Add the third row to the second row
ii. Subtract the third column from the first column.
The determinant of the resultant matrix is _____.
In the LU decomposition of the matrix , if the diagonal elements of U are both , then the lower diagonal entry of L is_________________.
Let the characteristic equation of matrix M be λ^{2}  λ  1 = 0 . Then
Consider the following statements:
• SI: The sum of two singularn n x n matrices may be nonsingular
• S2: The sum of two n x n nonsingular matrices may be singular
Which one of the following statements is correct?
How many 4 x 4 matrices with entries from have odd determinant?
Hint: Use modulo arithmetic.
Let A be an n × n matrix of the following form.
What is the value of the determinant of A?
If matrix and X^{2}  X + I = 0 (I is the identity matrix and is the zero matrix), then the inverse of X is
The number of different symmetric matrices with each element being either 0 or 1 is: (Note: (2,X) is same as 2^{X})
The rank of the following matrix, where is a real number is
Let A and B be real symmetric matrices of size. Then which one of the following is true?
Let A, B, C,D be n * n matrices, each with nonzero determinant. If ABCD = I, then B^{1} is
In an M × N matrix all nonzero entries are covered in rows and columns. Then the maximum number of nonzero entries, such that no two are on the same row or column, is
If M is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?
S1: Each row of M can be represented as a linear combination of the other rows
S2: Each column of M can be represented as a linear combination of the other columns
S3: MX = 0 has a nontrivial solution
S4: M has an inverse
Consider the following system of linear equations
Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of , does this system of equations have infinitely many solutions?
Consider the following system of linear equations :
The system of equations has
How many solutions does the following system of linear equations have?
Consider the following set of equations x + 2y = 54 x+8y = 123x + 6y+3z = 15. This set
150 docs216 tests

150 docs216 tests
