Find A^4 for Scalar Matrix Find A4 Given: \[ A = \begin{bmatrix} -3 & 0 \\ 0 & -3 \end{bmatrix} \] Step 1: Recognize the Matrix \[ A = -3I \] Step 2: Compute A4 \[ A^4 = (-3I)^4 = (-3)^4 I^4 \] \[ A^4 = 81I \] Final Answer: \[ A^4 = \begin{bmatrix} 81 […]
If A = [[-3, 0], [0, -3]], find A^4 Read More »
Find A^3 for -I Matrix Find A3 Given: \[ A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix} \] Step 1: Recognize the Matrix \[ A = -I \] Step 2: Compute A3 \[ A^3 = (-I)^3 = (-1)^3 I^3 \] \[ A^3
If A = [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], find A^3 Read More »
Find A^2 for -I Matrix Find A2 Given: \[ A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix} \] Step 1: Recognize the Matrix \[ A = -I \] Step 2: Compute A2 \[ A^2 = (-I)^2 = (-1)^2 I^2 \] \[ A^2
If A = [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], find A^2 Read More »
Find λ such that A^4 = λA Find λ such that A4 = λA Given: \[ A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \] Step 1: Find A2 \[ A^2 = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} = \begin{bmatrix}
If A = [[1, 1], [1, 1]] satisfies A^4 = λA, then write the value of λ. Read More »
Find k such that A^2 = kA Find k such that A2 = kA Given: \[ A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \] Step 1: Compute A2 \[ A^2 = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \] \[
If A = [[1, -1], [-1, 1]], satisfies the matrix equation A^2 = kA, write the value of k. Read More »
Find x and y in Matrix Equation Find x and y from Matrix Equation Given: \[ \begin{bmatrix} 1 & 0 \\ y & 5 \end{bmatrix} + 2\begin{bmatrix} x & 0 \\ 1 & -2 \end{bmatrix} = I \] \[ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] Step 1: Multiply the
If [[1, 0], [y, 5]] + 2[[x, 0], [1, -2]] = I, where I is 2×2 unit matrix. Find x and y. Read More »
Find AA^T for Trigonometric Matrix Find AAT Given: \[ A = \begin{bmatrix} \cos x & -\sin x \\ \sin x & \cos x \end{bmatrix} \] Step 1: Find AT \[ A^T = \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix} \] Step 2: Compute AAT \[ AA^T = \begin{bmatrix} \cos
If A = [[cos x, -sin x], [sin x, cos x]], find AA^T Read More »
Find x when A + A^T = I Find x such that A + AT = I Given: \[ A = \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix} \] Step 1: Find AT \[ A^T = \begin{bmatrix} \cos x & -\sin x \\ \sin x & \cos x \end{bmatrix}
Find A^2 for Complex Matrix Find A2 Given: \[ A = \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix} \] Step 1: Compute A2 = A × A \[ A^2 = \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix} \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix} \] \[ A^2 = \begin{bmatrix}
If A = [[i, 0], [0, i]], write A^2 Read More »
Find A + A^T Find A + AT Given: \[ A = \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} \] Step 1: Find AT \[ A^T = \begin{bmatrix} 2 & 5 \\ 3 & 7 \end{bmatrix} \] Step 2: Compute A + AT \[ A + A^T = \begin{bmatrix} 2 & 3 \\
If A = [[2, 3], [5, 7]], find A,+,A^T Read More »