Engineering Mathematics
Q81.
Consider the following system of equations: 3x + 2y = 1 4x + 7z = 1 x + y + z = 3 x - 2y + 7z = 0 The number of solutions for this system isQ82.
If the matrix A is such that \begin{bmatrix} 2\\ -4\\ 7 \end{bmatrix}\begin{bmatrix} 1 &9 &5 \end{bmatrix} Then the determinant of A is equal to ________.Q83.
Consider the matrix as given below. \begin{bmatrix} 1 & 2&3 \\ 0& 4 & 7\\ 0&0 & 3 \end{bmatrix} Which one of the following provides the CORRECT values of eigenvalues of the matrix?Q85.
Which one of the following does NOT equal \begin{bmatrix} 1 & x&x^{2} \\ 1& y & y^{2}\\ 1&z & z^{2} \end{bmatrix}?Q86.
Let A be the 2x2 matrix with elements a_{11}=a_{12}=a_{21}=+1 and a_{22}=-1. Then the eigenvalues of the matrix A^{19} areQ87.
A function f(x) is continuous in the interval [0,2]. It is known that f(0)=f(2)=-1 and f(1)=1. Which one of the following statements must be true?Q88.
What is the matrix that represents rotation of an object by \theta^0 about the origin in 2D?Q89.
Consider the following matrix.\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}The largest eigenvalue of the above matrix is __________.Q90.
Let X be a square matrix. Consider the following two statements on X. I. X is invertible II. Determinant of X is non-zero Which one of the following is TRUE?