(i) If A=1-202 130-21, find A−1. Using A−1, solve the system of linear equationsx − 2y = 10, 2x + y + 3z = 8, −2y + z = 7(ii) A=3-422 351 01, find A−1 and hence solve the following system of equations:3x − 4y + 2z = −1, 2x + 3y + 5z = 7, x + z = 2(iii) A=1-202130-21 and B=72-6-21-3-42 5, find AB. Hence, solve the system of equations:x − 2y = 10, 2x + y + 3z = 8 and −2y + z = 7(iv) If A=120-2 -1-20-11, find A−1. Using A−1, solve the system of linear equationsx − 2y = 10, 2x − y − z = 8, −2y + z = 7(v) Given A=22-4-42-42-1 5, B=1-10234012, find BA and use this to solve the system of equationsy + 2z = 7, x − y = 3, 2x + 3y + 4z = 17(vi) If A=2311 22–3 1-1, find A–1 and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8.(vii) Use product 1-1202-33-24-20192-361-2 to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3.

(i) If A=1-202 130-21, find A−1. Using A−1, solve the system of

1.	(i) If A=1-202 130-21, find A−1. Using A−1, solve the system of linear equationsx − 2y = 10, 2x + y + 3z = 8, −2y + z = 7(ii) A=3-422 351 01, find A−1 and hence solve the following system of equations:3x − 4y + 2z = −1, 2x + 3y + 5z = 7, x + z = 2(iii) A=1-202130-21 and B=72-6-21-3-42 5, find AB. Hence, solve the system of equations:x − 2y = 10, 2x + y + 3z = 8 and −2y + z = 7(iv) If A=120-2 -1-20-11, find A−1. Using A−1, solve the system of linear equationsx − 2y = 10, 2x − y − z = 8, −2y + z = 7(v) Given A=22-4-42-42-1 5, B=1-10234012, find BA and use this to solve the system of equationsy + 2z = 7, x − y = 3, 2x + 3y + 4z = 17(vi) If A=2311 22–3 1-1, find A–1 and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8.(vii) Use product 1-1202-33-24-20192-361-2 to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3.
Answer» (i) If $A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}]$ , find A⁻¹. Using A⁻¹, solve the system of linear equations x − 2y = 10, 2x + y + 3z = 8, −2y + z = 7 (ii) $A = [\begin{matrix} 3 & - 4 & 2 \\ 2 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$ , find A⁻¹ and hence solve the following system of equations: 3x − 4y + 2z = −1, 2x + 3y + 5z = 7, x + z = 2 (iii) $A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}] and B = [\begin{matrix} 7 & 2 & - 6 \\ - 2 & 1 & - 3 \\ - 4 & 2 & 5 \end{matrix}]$ , find AB. Hence, solve the system of equations: x − 2y = 10, 2x + y + 3z = 8 and −2y + z = 7 (iv) If $A = [\begin{matrix} 1 & 2 & 0 \\ - 2 & - 1 & - 2 \\ 0 & - 1 & 1 \end{matrix}]$ , find A⁻¹. Using A⁻¹, solve the system of linear equations x − 2y = 10, 2x − y − z = 8, −2y + z = 7 (v) Given $A = [\begin{matrix} 2 & 2 & - 4 \\ - 4 & 2 & - 4 \\ 2 & - 1 & 5 \end{matrix}], B = [\begin{matrix} 1 & - 1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{matrix}]$ , find BA and use this to solve the system of equations y + 2z = 7, x − y = 3, 2x + 3y + 4z = 17 (vi) If $A = (\begin{array}{rrr} 2 & 3 & 1 \\ 1 & 2 & 2 \\ - 3 & 1 & - 1 \end{array})$ , find A^–1 and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8. (vii) Use product $[\begin{matrix} 1 & - 1 & 2 \\ 0 & 2 & - 3 \\ 3 & - 2 & 4 \end{matrix}] [\begin{matrix} - 2 & 0 & 1 \\ 9 & 2 & - 3 \\ 6 & 1 & - 2 \end{matrix}]$ to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3.

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