9231 FP2 · Notes & worked examples
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
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 \(\displaystyle v=(x,y,z)^{T}\).
Find z.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
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 \(\displaystyle v=(x,y,z)^{T}\).
Find z.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
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 \(\displaystyle v=(x,y,z)^{T}\).
Find y.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
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 \(\displaystyle v=(x,y,z)^{T}\).
Find y.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
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.
Fresh review variant
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.
Check understanding
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 \(\displaystyle t=30\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
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 \(\displaystyle t=32\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.