Ravi Kant Kumar

Find λ in Matrix Equation Finding λ (Lambda) Question: Find the non-zero scalar \( \lambda \) if: \[ \lambda \begin{bmatrix} 1 & 0 & 2 \\ 3 & 4 & 5 \end{bmatrix} + 2 \begin{bmatrix} 1 & 2 & 3 \\ -1 & -3 & 2 \end{bmatrix} = \begin{bmatrix} 4 & 4 & 10 \\ […]

Find x and y from Matrix Equation Finding x and y Question: Solve: \[ 2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix} \] Solution: Step 1: Multiply the matrix \[ 2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} = \begin{bmatrix}6 &

Find x and y (Vector Matrix Equation) Finding x and y Question: Solve: \[ x\begin{bmatrix}2\\1\end{bmatrix} + y\begin{bmatrix}3\\5\end{bmatrix} + \begin{bmatrix}-8\\11\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \] Solution: Step 1: Expand the equation \[ \begin{bmatrix} 2x \\ x \end{bmatrix} + \begin{bmatrix} 3y \\ 5y \end{bmatrix} + \begin{bmatrix} -8 \\ 11 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \] Step 2:

Find x, y, z from Matrix Equation Finding x, y, z Question: Solve: \[ [x,\; y+2,\; z-3] + [y,\; 4,\; 5] = [4,\; 9,\; 12] \] Solution: Step 1: Add corresponding elements \[ [x+y,\; y+6,\; z+2] = [4,\; 9,\; 12] \] Step 2: Compare corresponding elements \[ x + y = 4 \quad …(1) \]

Find x and y from Matrix Equation Finding x and y Question: Solve: \[ \begin{bmatrix} x-y & 2 & -2 \\ 4 & x & 6 \end{bmatrix} + \begin{bmatrix} 3 & -2 & 2 \\ 1 & 0 & -1 \end{bmatrix} = \begin{bmatrix} 6 & 0 & 0 \\ 5 & 2x+y & 5 \end{bmatrix}

Find Matrix C (Zero Matrix Condition) Finding Matrix C Question: If \[ A=\begin{bmatrix}1 & -3 & 2 \\ 2 & 0 & 2\end{bmatrix}, \quad B=\begin{bmatrix}2 & -1 & -1 \\ 1 & 0 & -1\end{bmatrix} \] find matrix \(C\) such that: \[ A + B + C = 0 \] Solution: Step 1: Rearrange the

Find Matrix X (2A + 3X = 5B) Finding Matrix X Question: If \[ A=\begin{bmatrix}2 & -2 \\ 4 & 2 \\ -5 & 1\end{bmatrix}, \quad B=\begin{bmatrix}8 & 0 \\ 4 & -2 \\ 3 & 6\end{bmatrix} \] find matrix \(X\) such that: \[ 2A + 3X = 5B \] Solution: Step 1: Rearrange the

Find Matrix C (Null Matrix Condition) Finding Matrix C Question: If \[ A=\begin{bmatrix}9 & 1 \\ 7 & 8\end{bmatrix}, \quad B=\begin{bmatrix}1 & 5 \\ 7 & 12\end{bmatrix} \] find matrix \(C\) such that: \[ 5A + 3B + 2C = 0 \] Solution: Step 1: Rearrange the equation \[ 2C = -(5A + 3B) \]

Find Matrix A Finding Matrix A Question: If \[ \begin{bmatrix} 1 & 2 & -1 \\ 0 & 4 & 9 \end{bmatrix} + A = \begin{bmatrix} 9 & -1 & 4 \\ -2 & 1 & 3 \end{bmatrix} \] find matrix \(A\). Solution: Step 1: Rearrange the equation \[ A = \begin{bmatrix} 9 & -1

Find Matrices X and Y (3×3) Finding Matrices X and Y (3×3) Question: If \[ X – Y = \begin{bmatrix} 1 & 1 & 1\\ 1 & 1 & 0\\ 1 & 0 & 0 \end{bmatrix}, \quad X + Y = \begin{bmatrix} 3 & 5 & 1\\ -1 & 1 & 4\\ 11 & 8