Systems of equations: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(A v=b\) where \(A=\left[\begin{matrix}1 & 1 & 1\\0 & 12 & 1\\0 & 0 & 13\end{matrix}\right],\ b=\left[\begin{matrix}39\\171\\195\end{matrix}\right]\) and v=(x,y,z)ᵀ.
Find z.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(A v=b\) where \(A=\left[\begin{matrix}1 & 1 & 1\\0 & 13 & 1\\0 & 0 & 14\end{matrix}\right],\ b=\left[\begin{matrix}42\\198\\224\end{matrix}\right]\) and v=(x,y,z)ᵀ.
Find z.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: check 2
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(A v=b\) where \(A=\left[\begin{matrix}1 & 1 & 1\\0 & 13 & 1\\0 & 0 & 14\end{matrix}\right],\ b=\left[\begin{matrix}42\\198\\224\end{matrix}\right]\) and v=(x,y,z)ᵀ.
Find y.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(A v=b\) where \(A=\left[\begin{matrix}1 & 1 & 1\\0 & 14 & 1\\0 & 0 & 15\end{matrix}\right],\ b=\left[\begin{matrix}45\\227\\255\end{matrix}\right]\) and v=(x,y,z)ᵀ.
Find y.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Let \(A(t)=\left[\begin{matrix}1 & 1 & 1\\1 & t - 12 & 2\\2 & 2 & t - 11\end{matrix}\right]\). In the singular case consider right-hand side \((15,29,c)^T\). For the separate nonsingular calculation set \(t=15\) and use \(b=\left[\begin{matrix}43\\87\\118\end{matrix}\right]\).
Find x in the specified nonsingular system.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Let \(A(t)=\left[\begin{matrix}1 & 1 & 1\\1 & t - 13 & 2\\2 & 2 & t - 12\end{matrix}\right]\). In the singular case consider right-hand side \((16,31,c)^T\). For the separate nonsingular calculation set \(t=16\) and use \(b=\left[\begin{matrix}46\\93\\126\end{matrix}\right]\).
Find x in the specified nonsingular system.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: check 4
Difficulty: ★★☆Maths4U Original · Short practice
Let \(A(t)=\left[\begin{matrix}1 & 1 & 1\\1 & t - 13 & 2\\2 & 2 & t - 12\end{matrix}\right]\). In the singular case consider right-hand side \((16,31,c)^T\). For the separate nonsingular calculation set \(t=16\) and use \(b=\left[\begin{matrix}46\\93\\126\end{matrix}\right]\).
Find the determinant at t=30.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Systems of equations: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
Let \(A(t)=\left[\begin{matrix}1 & 1 & 1\\1 & t - 14 & 2\\2 & 2 & t - 13\end{matrix}\right]\). In the singular case consider right-hand side \((17,33,c)^T\). For the separate nonsingular calculation set \(t=17\) and use \(b=\left[\begin{matrix}49\\99\\134\end{matrix}\right]\).
Find the determinant at t=32.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.