Question

Circle your answer and justify it by showing your work. (a) T F: (b) T F: Let A be any square matrix, then ATA, AAT, and A + AT are all symmetric. If S is invertible, then ST is also invertible. If a row exchange is required to reduce matrix A into upper triangular form U, then (c) T F: A can not be factored as A = LU. (d) T F: Suppose A reduces to upper triangular U but U has a 0 in pivot position, then A has no LDU factorization. (e) T F: If A2 is not invertible, then A is not invertible. 10 10. [10points] (a) T F: All(x,y,z)∈R3 withx=y+z+1isasubspaceofR3 (b) T F: All(x,y,z)∈R3 withx+z=0isasubspaceofR3 (c) T F: All 2 × 2 symmetric matrices is a subspace of M22. (Here M22 is the vector space of all 2 × 2 matrices.) (d) T F: All polynomials of degree exactly 3 is a subspace of P5. (Here P5 is the vector space of all polynomials a5x5 + a4x4 + a3x3 + a2x2 + a1x + a0 of degree less than or equal to 5.) (e) T F: P3 is a subspace of P5. (Here Pi is the vector space of all polynomials aixi+ai−1xi−1+ ai−2x1−2 + ... + a2x2 + a1x + a0 of degree less than or equal to i.)a. TrueB. False.

Answer 1

Answer:

a-True

b-True

c-True

d- False

e-True

f-True

g-True

h- False

i-True

j- False

Step-by-step explanation:

See the attached pictures.