Stitz-Zeager_College_Algebra_e-book

# Those two numbers are called the eigenvalues of c the

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Unformatted text preview: A2 − B 2 = −9 −12 1 −2 (i) (A + B )(A − B ) = (g) A − 4I2 = 238 3 863 15 −3 2 30 00 00 −30 20 −15 0 0 −36 (k) E 2 + 5E − 36I3 = 0 0 −36 3449 − 407 99 15 6 (l) EDC = − 9548 − 101 −648 15 3 −324 −35 −360 −126 361 5 (m) CDE is undeﬁned (n) ABCEDI2 = − 90749 15 − 28867 5 − 156601 15 − 47033 5 def E1 interchanged R1 and R2 of A. abc 5a 5b 5c E2 multiplied R1 of A by 5. E2 A = def a − 2d b − 2e c − 2f E3 replaced R1 in A with R1 − 2R2. E3 A = d e f 1 0 E4 = 0 −6 2. E1 A = −7 3 46 2 (j) A2 − 5A − 2I2 = (d) E + D is undeﬁned 67 11 3 (e) ED = − 178 −72 3 −30 −40 (f) CD + 2I2 A = −8 16 25 3 8.4 Systems of Linear Equations: Matrix Inverses 8.4 493 Systems of Linear Equations: Matrix Inverses We concluded Section 8.3 by showing how we can rewrite a system of linear equations as the matrix equation AX = B where A and B are known matrices and the solution matrix X of the equation corresponds to the solution of the system. In this se...
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