Sample Quiz on Matrix Algebra Question # 1: The product of two upper triangular matrices is: Select Answer Here (a) an upper triangular matrix (b) a lower triangular matrix (c) a symmetric matrix (d) a diagonal matrix Question # 2: The echelon form of an augmented matrix of a system of linear equations is given by A = matrix([[1,0,1,a1],[0,1,2,a2-3*a1],[0,0,0,a3-2*a2+a1]]); Then the system has infinitely many solutions if: Select Answer Here (a) a1,a2,a3 arbitrary (b) a1-a2-a3=0 (c) a3=2*a2+a1 (d) a3=2*a2-a1 Question # 3: A is a matrix such that its cube is equal to itself. Then: Select Answer Here (a) A can only be the zero matrix (b) A can only be the identity matrix (c) A can only be invertible (d) A to the power 15 is A Question # 4: The matrices A = matrix([[1,x+y,z],[2,x-y,4]]); B = matrix([[x,z,6],[z-4,-4,4]]); Select Answer Here (a) are equal if x=1,y=z=6 (b) are equal if x=1,y=5,z=6 (c) are equal if x=1,y=-5,z=6 (d) are not equal for any values of x,y, and z Question # 5: The product of an nxr matrix A and rxm matrix B is Select Answer Here (a) an mxr matrix (b) an nxm matrix (c) not defined (d) rxn matrix Question # 6: The (3,2) entry in the product of the two matrices A=matrix([[1,2,0],[-3,2,1],[3,1,3]]); B=matrix([[1,2],[-3,2],[1,5]])); Select Answer Here (a) is -23 (b) is 23 (c) is 6 (d) is 15 Question # 7: Which one of the following statements is correct? Select Answer Here (a) The sum of two nxm matrices is an nxm matrix (b) The product of any two matrices is well defined (c) Multiplication of matrices, whenever defined,is commutative (d) Addition of matrices whenever defined is not commutative Question # 8: Which one of the following statements is not correct? Select Answer Here (a) The sum of two nxm matrices is an nxm matrix (b) The product of an nxm matrix and an mxn matrix is well defined (c) Multiplication of matrices, whenever defined, is commutative (d) Addition of matrices whenever defined is commutative