ENGINEERING MATHEMATICS MATRIX



1. Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are 

(a) 1024 and − 1024 

(b) 1024√2 and −1024√2 

(c) 4√2 and − 4√2 

(d) 512√2 and − 512√2

2. The product of the non-zero eigenvalues of the matrix: 

1 0 0 0 1

0 1 1 1 0 

0 1 1 1 0

0 1 1 1 0

1 0 0 0 1

 is _____________. 

(a) 4    (b) 5     (c) 6       (d) 7 


3. Consider the following system of equations in three real variables xl , x2 and x3 

2×1 – x2 + 3×3 = 1

 3×1– 2×2 + 5×3 = 2 

–x1 + 4×2 + x3 = 3 

This system of equation has 

(a) no solution

 (b) a unique solution

 (c) more than one but a finite number of solutions

 (d) an infinite number of solutions 

                                                                    


4. Let A, B, C, D be n × n matrices, each with non-zero determinant. If ABCD = 1, then B-1 is

 (a) D-1C -1A -1 

(b) CDA 

(c) ADC 

(d) Does not necessarily exist 


5. How many solutions does the following system of linear equations have?

 − x + 5y = −1

 x − y = 2 

 x + 3y = 3 

(a) infinitely many 

(b) two distinct solutions 

(c) unique 

(d) none of these

6. In an M’N matrix such that all non-zero entries are covered in a rows and b columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is: 

(a) ≤ a + b

 (b) ≤ max {a, b}

 (c) ≤ min {M-a, N-b} 

(d) ≤ min {a, b}


7. Consider the following statements: S1: The sum of two singular n × n matrices may be non-singular S2: The sum of two n × n non-singular matrices may be singular. 

Which of the following statements is correct? 

(a) S1 and S2 are both true 

(b) S1 is true, S2 is false

 (c) S1 is false, S2 is true 

(d) S1 and S2 are both false 

                                      

8. In the LU decomposition of the matrix

 | 2 2 |

 | 4 9 |

 if the diagonal elements of U are both 1, then the lower diagonal entry I22 of L is 

(a) 4       (b) 5       (c) 6      (d) 7 


9. If the following system has non-trivial solution, 

px + qy + rz = 0

 qx + ry + pz = 0 

rx + py + qz = 0 

then which one of the following options is True? 

(a) p – q + r = 0 or p = q = –r 

(b) p + q – r = 0 or p = –q = r 

(c) p + q + r = 0 or p = q = r 

(d) p – q + r = 0 or p = –q = –r

 

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