Educational

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 –

Find x and y by Equating Matrices Find x and y Given: \[ \begin{bmatrix} x+3 & 4 \\ y-4 & x+y \end{bmatrix} = \begin{bmatrix} 5 & 4 \\ 3 & 9 \end{bmatrix} \] Step 1: Compare Corresponding Elements \[ x + 3 = 5 \Rightarrow x = 2 \] \[ y – 4 = 3

Find x and y from Matrix Equation Find x and y Given: \[ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} \] Step 1: Multiply the First Matrix \[ 2\begin{bmatrix} 1 & 3 \\

Matrix Both Symmetric and Skew-Symmetric Matrix that is Both Symmetric and Skew-Symmetric Condition: \[ A^T = A \quad \text{(symmetric)} \] \[ A^T = -A \quad \text{(skew-symmetric)} \] Step: Combine Both \[ A = -A \Rightarrow 2A = 0 \Rightarrow A = 0 \] Final Answer: \[ A = \begin{bmatrix} 0 & 0 \\ 0 &