Ravi Kant Kumar

Find k from Matrix Multiplication Find k Given: \[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 3 & 1 \\ 2 & 5 \end{bmatrix} = \begin{bmatrix} 7 & 11 \\ k & 23 \end{bmatrix} \] Step 1: Multiply Matrices \[ AB = \begin{bmatrix} 1(3) + 2(2) & 1(1) + 2(5) \\ 3(3) […]

Find α when Matrix is Identity Find α such that Matrix is Identity Given: \[ A = \begin{bmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{bmatrix} \] \[ A = I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] Step 1: Compare Elements \[ \cos \alpha = 1

Order of Matrix AB Find the Order of Matrix AB Given: \[ A \text{ is of order } 3 \times 4,\quad B \text{ is of order } 4 \times 3 \] Step 1: Check Multiplication Condition \[ \text{Number of columns of A} = \text{Number of rows of B} = 4 \] So, AB exists. Step

Find a from Matrix Equation Find a Given: \[ \begin{bmatrix} a + b & 2 \\ 5 & b \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 2 & 2 \end{bmatrix} \] Step 1: Compare Elements \[ b = 2 \] \[ a + b = 6 \] Step 2: Substitute b \[ a + 2

Find A + A^T Find A + AT Given: \[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \] Step 1: Find AT \[ A^T = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \] Step 2: Add Matrices \[ A + A^T = \begin{bmatrix} 1 & 2 \\ 3 &

Find x from Matrix Equation Find x Given: \[ \begin{bmatrix} 2x + y & 3y \\ 0 & 4 \end{bmatrix} = \begin{bmatrix} 6 & 0 \\ 6 & 4 \end{bmatrix} \] Step 1: Compare Corresponding Elements \[ 3y = 0 \Rightarrow y = 0 \] \[ 2x + y = 6 \] Step 2: Substitute

Find AA^T for Row Matrix Find AAT Given: \[ A = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \] Step 1: Find AT \[ A^T = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \] Step 2: Multiply AAT \[ AA^T = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}

Find x from Matrix Equation Find x Given: \[ \begin{bmatrix} 3x + y & -y \\ 2y – x & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} \] Step 1: Compare Elements \[ -y = 2 \Rightarrow y = -2 \] \[ 2y – x = -5 \] Step 2:

Find y from Matrix Equation Find y Given: \[ \begin{bmatrix} x – y & 2 \\ x & 5 \end{bmatrix} = \begin{bmatrix} 2 & 2 \\ 3 & 5 \end{bmatrix} \] Step 1: Compare Corresponding Elements \[ x = 3 \] \[ x – y = 2 \] Step 2: Substitute x \[ 3 –

Find x from Matrix Equation Find x Given: \[ \begin{bmatrix} 2x – y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix} \] Step 1: Compare Corresponding Elements \[ y = -2 \] \[ 2x – y = 6 \] Step 2: Substitute y \[ 2x –