Solution: Given that $x+y-6 z=0$ $\begin{array}{l} x-y+2 z=0 \\ -3 x+y+2 z=0 \end{array}$ We can write the system as $\begin{array}{l} {\left[\begin{array}{ccc} 1 & 1 & -6 \\ 1 & -1...

Solution: Given that $3 x-y+2 z=0$ $\begin{array}{l} 4 x+3 y+3 z=0 \\ 5 x+7 y+4 z=0 \end{array}$ We can write the system as $\begin{array}{l} {\left[\begin{array}{ccc} 3 & -1 & 2 \\ 4 &...

Solution: Given that $2 x-y+2 z=0$ $\begin{array}{l} 5 x+3 y-z=0 \\ x+5 y-5 z=0 \end{array}$ We can write the system as $\begin{array}{l} {\left[\begin{array}{ccc} 2 & -1 & 2 \\ 5 & 3...

Solution: It is given that $\begin{array}{l} 2 x-y+z=0 \\ 3 x+2 y-z=0 \\ x+4 y+3 z=0 \end{array}$ We can write the system as $\left[\begin{array}{ccc} 2 & -1 & 1 \\ 3 & 2 & -1 \\ 1...

Solution: Suppose the numbers as $x$, $y$, and $z$ $x+y+z=10,000 \ldots \ldots \text { (i) }$ Also, $0.1 \mathrm{x}+0.12 \mathrm{y}+0.15 z=1310 \ldots \ldots \text { (ii) }$ Again, $0.1 x+0.12...

Solution: Suppose the numbers as $x$, $y$, $z$ $\begin{array}{l} x+y+z=2 \\ \ldots \cdots(i) \end{array}$ Also, $2 y+(x+z)+1$ $x+2 y+z=1 \ldots \ldots \text { (ii) }$ Again, $\begin{array}{l}...

Solution: Given that $\begin{array}{l} B=\left[\begin{array}{ccc} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{array}\right]_{A}=\left[\begin{array}{ccc} 2 & 2 & -4 \\...

(i) Solution: $\begin{array}{l} A=\left[\begin{array}{ccc} 1 & -2 & 0 \\ 2 & 1 & 3 \\ 0 & -2 & 1 \end{array}\right]_{B}=\left[\begin{array}{ccc} 7 & 2 & -6 \\ -2...

(i) Solution: Given that $\begin{array}{l} A=\left[\begin{array}{ccc} 1 & -2 & 0 \\ 2 & 1 & 3 \\ 0 & -2 & 1 \end{array}\right] \\ |A|=1(1+6)+2(2-0)+0 \\ =7+4 \\ =11...

Solution: Given that $\begin{array}{l} A=\left[\begin{array}{ccc} 1 & 2 & 5 \\ 1 & -1 & -1 \\ 2 & 3 & -1 \end{array}\right] \\ |\mathrm{A}|=1(1+3)+2(-1+2)+5(3+2) \\ =4+2+25...

Solution: $\begin{array}{r} A=\left[\begin{array}{ccc} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{array}\right] \\ |\mathrm{A}|=2(0)+3(-2)+5(1) \\ =-1 \end{array}$ Now, the...

Solution: $\begin{array}{l} A=\left[\begin{array}{ccc} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{array}\right]_{B}=\left[\begin{array}{ccc} 2 & 2 & -4 \\ -4 & 2...

Solution: (i) Given that $3 x-y-2 z=2$ $\begin{array}{l} 2 y-z=-1 \\ 3 x-5 y=3 \\ {\left[\begin{array}{ccc} 3 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0...

Solution: (i) Given that $4 x-2 y=3$ $6 x-3 y=5$ We can write the above system of equations as $\left[\begin{array}{ll} 4 & -2 \\ 6 & -3 \end{array}\right]\left[\begin{array}{l} \mathrm{X}...

Solution: (i) Given that $2 x+5 y=7$ $6 x+15 y=13$ We can write the above system of equations as $\left[\begin{array}{cc} 2 & 5 \\ 6 & 15 \end{array}\right]\left[\begin{array}{l} \mathrm{X}...

Solution: (i) Given that $x+y+z=6$ $\begin{array}{l} x+2 y+3 z=14 \\ x+4 y+7 z=30 \end{array}$ We can write this as $\begin{array}{l} {\left[\begin{array}{ccc} 2 & 2 & -2 \\ 4 & 4 &...

Solution: (i) Given that$5 x+3 y+7 z=4$ $\begin{array}{l} 3 x+26 y+2 z=9 \\ 7 x+2 y+10 z=5 \end{array}$ We can write this as: $\begin{array}{l} {\left[\begin{array}{ccc} 5 & 3 & 7 \\ 3 &...

Solution: (i) Given that $6 x+4 y=2$ $9 x+6 y=3$ We can write the above system of equations as $\left[\begin{array}{ll} 6 & 4 \\ 9 & 6 \end{array}\right]\left[\begin{array}{l} \mathrm{X} \\...

Solution: (i) Given that $(2 / x)+(3 / y)+(10 / z)=4$ $\begin{array}{l} (4 / x)-(6 / y)+(5 / z)=1 \\ (6 / x)+(9 / y)-(20 / z)=2, x, y, z \neq 0 \end{array}$ We can write the given system in matrix...

Solution: (i) Given that $8 x+4 y+3 z=18$ $\begin{array}{l} 2 x+y+z=5 \\ x+2 y+z=5 \end{array}$ We can write the given system in matrix form as: $\begin{array}{l} {\left[\begin{array}{lll} 8 & 4...

Solution: (i) Given that $2 x+6 y=2$ $\begin{array}{l} 3 x-z=-8 \\ 2 x-y+z=-3 \end{array}$ We can write the given system in matrix form as: $\begin{array}{c} {\left[\begin{array}{ccc} 2 & 6...

Solution: (i) Given that $3 x+4 y+2 z=8$ $\begin{array}{l} 2 y-3 z=3 \\ x-2 y+6 z=-2 \end{array}$ We can write the given system in matrix form as: $\left[\begin{array}{rrr} 2 & 1 & 1 \\ 1...

Solution: (i) Given that $(2 / x)-(3 / y)+(3 / z)=10$ $\begin{array}{l} (1 / x)+(1 / y)+(1 / z)=10 \\ (3 / x)-(1 / y)+(2 / z)=13 \end{array}$ We can write the given system in matrix form as:...

Solution: (i) Given that $6 x-12 y+25 z=4$ $\begin{array}{l} 4 x+15 y-20 z=3 \\ 2 x+18 y+15 z=10 \end{array}$ We can write the given system in matrix form as: $\left[\begin{array}{ccc}6 & -12...

Solution: (i) Given that $x+y-z=3$ $\begin{array}{l} 2 x+3 y+z=10 \\ 3 x-y-7 z=1 \end{array}$ We can write the given system in matrix form as: $\begin{array}{c} {\left[\begin{array}{ccc} 1 & 1...

Solution: (i) Given that $3 x+7 y=4$ $x+2 y=-1$ We can write the above system of equations as $\left[\begin{array}{ll} 3 & 7 \\ 1 & 2 \end{array}\right]\left[\begin{array}{l} \mathrm{X} \\...

Solution: (i) Given that $3 x+4 y-5=0$ $x-y+3=0$ We can write the above system of equations as $\left[\begin{array}{cc} 3 & 4 \\ 1 & -1 \end{array}\right]\left[\begin{array}{l} \mathrm{X} \\...

Solution: (i) Given that $5 x+7 y+2=0$ and $4 x+6 y+3=0$ We can write the above system of equations as $\left[\begin{array}{ll} 5 & 7 \\ 4 & 6 \end{array}\right]\left[\begin{array}{l}...