Question: (d) Use the definition below to determine whether B is positive definite. (6) Definition: A square matrix B of order n 2 1 is said

(d) Use the definition below to determine whether B is positive definite. (6) Definition: A square matrix B of order n 2 1 is said to be positive definite if there exists a column vector x = [X1 12 . .. In] # On such that x Bx > 0. 2 1 -3 B = 0 -4 3 4 -2 Explain Solution below step by step and why its not positive define please? x Bx = 2x1 - 12 + 3x3 X1 + 4x4 - 3x1 - 4.x2 - 2x3] T2 T3 = (2x1 - 12 + 3.13) 21+ (x1 + 4x4) 12 + (-31 - 4.12 - 2.13) 13 = 2x3 + 4x204 - 4x203 - 2x3 = 2(1 + 2)2 + 2(12 - 23)2 - 4(x3 - x3). Clearly, this expression is not strictly positive. It follows that the matrix B is NOT positive definite
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
