Assignment NO. 1 week2-week4 Student Full Name:___________________________________ . Student ID:__________________________________________ . CRN...

Assignment NO. 1 week2 -week4 Student Full Name :___________________________________ . Student ID :__________________________________________ . CRN No :____________________________________________ . Branch: _____________________________________________. Total Points True/False MCQ Short Answer ____/6 ____/6 ____/18 Total ____/30 Linear Algebra (Math -251) Due Date Date: 12 -03 -2017 Max. Marks :30 SECTION -I State whether the following statements are true or false : [× = ] (a) Regardless of the value of , the linear system − = 2 & 3− 3 = can not have unique solution. (a)……………. (b) If and are 3×3 matrices , then = . (b)……………. (c) Matrix = [ 2 1 3 4 2 1 4 2 6 ] is not invertible. (c)……………... (d) The product of tw o symmetric matrices is always s ymmetric . (d)…………….. (e) If and are invertible matrices of same size, then is invertible and ( )−1= −1−1. (e)…………….. (f) If and are square matrices of same size such that det ()= det (), then det ( + )= 2det () (f)……………... SECTION -II Select one of the alternatives from the following questions as your answer - [× = ] (a) A single linear equation with two or more unknowns must always has (A) No solution (B) Unique solution (C) Infinitely many solutions (D) None of the above Page 1 of 6 MATH 251 Department of Mathematics (b) If is a 6×4 matrix and is an × matrix such that is a 2×6 matrix, then the values of are (A) = 2, = 4 (B) = 4, = 2 (C) = 6, = 2 (D) = 2, = 6 (c) If = [1 2 2 4] , then (A) −1= [4 −2 −2 1 ] (B) −1= [4 2 2 1] (C) −1= [−1 2 2 −4] (D) −1 does not exi st (d) The transpose of upper triangular matrix is (A) Upper triangular matrix (B) Lower triangular matrix (C) Any matrix (D) Does not exi st (e) If = [1 3 2 5], then det (3) is (A) −3 (B) 6 (C) 9 (D) −9 (f) If = [2 3 1 4], then is equal to (A) [13 14 12 17 ] (B) [13 14 11 17 ] (C) [13 14 14 17 ] (D) [13 14 13 17 ] Section -II (Multiple Choice Questions) MCQ 1 2 3 4 5 6 Answers Page 2 of 6 MATH 251 Department of Mathematics SECTION -III Attempt all the question s - 1. Solve the following linear system by Gauss elimination method - [4] + + 2= 8 −− 2+ 3= 1 3− 7+ 4= 10 2. If = [4 5 5 3], = [6 8 10 4], and = [1 1 7 7]. Find AT+ 1 2B− C . [2] Page 3 of 6 MATH 251 Department of Mathematics 3. Solve the following linea r system of equations using A−1, [3] 2+ 3 = 10 + 2 = 6 4. Verify Associative law of matrix multiplication (i.e. ( )= ( )) by taking = [ 1 2 3 4 0 1 ], = [4 3 2 1], and = [1 0 2 3]. [3] Page 4 of 6 MATH 251 Department of Mathematics 5. Decide whether the given matrix is Invertible and if so, find its inverse using any method [3] = [ 2 5 5 −1 −1 0 2 4 3 ] Page 5 of 6 MATH 251 Department of Mathematics 6. Solve the following system of linear equations using Cramer’s rule. [3] −− 2= −8 + 3= 2 7+ + = 0 Page 6 of 6