Find b from Matrix Equation Find b Given: \[ \begin{bmatrix} a – b & 2a + c \\ 2a – b & 3c + d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix} \] Step 1: Form Equations \[ a – b = -1 \quad (1) \] \[ 2a – b = […]
If [[a – b, 2a + c], [2a – b, 3c + d]] = [[-1, 5], [0, 13]], find the value of b. Read More »
Find Matrix A Find Matrix A Given: \[ \begin{bmatrix} 9 & -1 & 4 \\ -2 & 1 & 3 \end{bmatrix} = A + \begin{bmatrix} 1 & 2 & -1 \\ 0 & 4 & 9 \end{bmatrix} \] Step 1: Rearrange \[ A = \begin{bmatrix} 9 & -1 & 4 \\ -2 & 1 &
If [[9, -1, 4], [-2, 1, 3]] = A + [[1, 2, -1], [0, 4, 9]], hen find matrix A. Read More »
Find x from Vector Equation Find x Given: \[ x\begin{bmatrix} 2 \\ 3 \end{bmatrix} + y\begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix} \] Step 1: Form Equations \[ 2x – y = 10 \] \[ 3x + y = 5 \] Step 2: Add Equations \[ (2x – y) + (3x
If x[[2], [3]] + y[[-1], [1]] = [[10], [5]], find the value of x. Read More »
Find a12 from aij = i/j Find a12 Given: \[ a_{ij} = \frac{i}{j}, \quad A \text{ is } 2 \times 2 \] Step 1: Identify Indices \[ a_{12} = \frac{1}{2} \] Final Answer: \[ \boxed{\frac{1}{2}} \] Next Question / Full Exercise
Possible Orders of Matrix with 5 Elements Possible Orders of a Matrix with 5 Elements Step 1: Use Formula \[ \text{Number of elements} = \text{rows} \times \text{columns} \] \[ m \times n = 5 \] Step 2: Factorize 5 \[ 5 = 1 \times 5 = 5 \times 1 \] Step 3: Possible Orders \[
If a matrix has 5 elements, write all possible orders it can have. Read More »
Find y from Matrix Equation Find y Given: \[ \begin{bmatrix} x & x – y \\ 2x + y & 7 \end{bmatrix} = \begin{bmatrix} 3 & 1 \\ 8 & 7 \end{bmatrix} \] Step 1: Compare Elements \[ x = 3 \] \[ x – y = 1 \] Step 2: Substitute x \[ 3
If [[x, x – y], [2x + y, 7]] = [[3, 1], [8, 7]], then find the value of y. Read More »
Number of 2×2 Matrices with 0 and 1 Total Number of 2×2 Matrices with Entries 0 and 1 Step 1: Understand the Matrix \[ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] Step 2: Possible Values Each entry can be either 0 or 1. \[ \text{Choices for each entry} = 2 \] Step
What is the total number of 2×2 matrices with each entry 0 and 1 ? Read More »
Find Order of Matrix B Find the Order of Matrix B Given: \[ A \text{ is of order } 2 \times 3 \] Step 1: Find AT \[ A^T \text{ is of order } 3 \times 2 \] Step 2: Condition for ATB \[ A^T (3 \times 2) \cdot B \Rightarrow \text{columns of } A^T
Find Symmetric Matrix B Find Symmetric Matrix B Given: \[ A = \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix} \] Formula: \[ B = \frac{1}{2}(A + A^T) \] Step 1: Find AT \[ A^T = \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix} \] Step 2: Compute A + AT \[ A
Evaluate (I + A)^2 – 3A Evaluate (I + A)2 − 3A Given: \[ A^2 = A \] Step 1: Expand \[ (I + A)^2 = I^2 + IA + AI + A^2 \] \[ = I + A + A + A^2 \] \[ = I + 2A + A^2 \] Step 2: Use