SOLUTION: steps and solution how to solve this question: M is the matrix (3 4) (p q) If M is a singular matrix and p=2,calculate the value of q.

Question 940542: steps and solution how to solve this question:
M is the matrix (3 4)
(p q)
If M is a singular matrix and p=2,calculate the value of q.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
M is the matrix

If is a singular matrix and ,calculate the value of :
A square matrix which does not have an inverse. A matrix is and its is .
so,
substitute

check:

Solved by pluggable solver: Finding the Determinant of a 2x2 Matrix

If you have the general 2x2 matrix:

the determinant is:

So this means that

Note: the vertical bars denote a determinant.

-----------------------------------------------------------------

So in this case the determinant of is:

Note: if you are having trouble with the fractions, check out this solver

======================================================

Answer:

So which means that the determinant of the matrix is 0

RELATED QUESTIONS
Proof of a singular matrix: I need to show (in general) that either matrix A is... (answered by venugopalramana,robertb)

Given P = ( 3 0 2 2 1 2 -3 -4 -6 ) a) if ( 2 6 n -2 m 9 0 -2 1 ) is the... (answered by ElectricPavlov)

Find k such that the matrix, M = [-3, 0, -3] [3, 2, 5] [-6+k, -2, -11] is... (answered by ikleyn)

Two matrices can be multiplied only if their sizes are compatible. Suppose that U is an m (answered by greenestamps)

What is the determinant of the matrix F and G F= 0 3 0 0 0 a 2 b c d (answered by ikleyn,math_tutor2020)

This homework problem has been stumping me. I am given this matrix: Matrix M =... (answered by Fombitz)

Find the following matrix(A) is non - singular, if so invert it. A=[3 1] 2 4 If (answered by Edwin McCravy)

hello! I tried my best to input the question, I'm unsure if there is a better way to type (answered by math_tutor2020)

if A= ( matrix( 3, 3, 0, 1, 0, 0, 0, 1, 5, 0, 0 ) ) then A^3= 5I and A is... (answered by ikleyn)