AP Calculus BC | CBSE Class 12 Maths | Solving for 'x' in a Row Matrix times Column Matrix Equation

Описание: Let's tackle another example of finding an unknown variable through matrix multiplication! In this video, we'll determine the value of 'x' from the equation where a matrix with row (-3, 2) multiplied by a matrix with column (-1, x) equals 1.
You'll learn:
1. How to perform the multiplication of a row matrix by a column matrix, resulting in a single numerical value.
2. The process of setting this matrix product equal to a given scalar to form a simple algebraic equation.
3. A clear, step-by-step demonstration of solving the resulting linear equation to find the value of 'x'.
This tutorial is perfect for reinforcing your understanding of basic matrix operations and translating them into solvable algebraic problems! #matrices #linearalgebra #matrixmultiplication #rowmatrix #columnmatrix #math #tutorial

Problem: Find x if the product of matrix A with row (-3, 2) and matrix B with column (-1, x) equals 1.
This video is suitable for students studying AP Calculus BC (US curriculum) and CBSE Class 12 Maths (Indian curriculum).

Solution:
Let the given matrices be:
A = | -3 2 | (This is a 1x2 matrix)

B = | -1 | (This is a 2x1 matrix)
| x |

We are given the matrix multiplication: AB = 1

For matrix multiplication AB, the number of columns in A (2) must equal the number of rows in B (2). The resulting matrix will have dimensions (rows of A) x (columns of B), which is 1x1.

AB = [ (-3 * -1) + (2 * x) ]

Perform the multiplication:
AB = [ 3 + 2x ]

We are given that this result equals 1:
[ 3 + 2x ] = [ 1 ]

Equating the elements, we get a linear equation:
3 + 2x = 1
2x = 1 - 3
2x = -2
x = -2 / 2
x = -1

The final answer is:
x = -1

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