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Mathematics SL Portfolio Assignment 1 Title: Matrix Powers Type 1 1. Consider the matrix M = Calculate Mn for n = 2, 3, 4, 5, 10, 20, 50. M²= * = = M³=*== M4=*== M5=*== M¹°=*== M²°=*== M5°=*== * To obtain the matrices above I multiplied (a*b+b*g), (a*f+b*h), (c*e+d*g), (c*f+d*h)as shown in the general formula seen below Describe in words any pattern you observe. In the above matrices the pattern I observed is shown in relationship to the exponents and the numbers within the matrix. As the exponent increases consecutively the matrix is in turn multiplied by two. Use this pattern to find a general expression for the matrix Mn in terms of n. As a result of the pattern expressed, the General Formula for these matrices is Mn=M*2n-¹ ......................................................................................................................................................................... 2. Consider the matrices P = and S = Calculate Pn and Sn for other values of n and describe any pattern(s) you observe. P²=*== Determinant: 100-36=64 P³=*= = Determinant: 1296-784=512 P4=*== Determinant: 18496-14400=4096 P5=*= Determinant: 278784-246016=32768 S²=*==...

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