Slide 1

• Topic: Determinants - Solved Examples – 1×1 matrix
• Overview:
  • Introduction to determinants
  • Explanation of 1×1 matrix
• Learning Objectives:
  • Understand the concept of determinants
  • Solve problems related to 1×1 matrices

Slide 2

• Determinants:
  • A determinant is a mathematical object that is defined for a square matrix.
  • It is denoted by |A| or det(A).
  • The determinant of a 1×1 matrix (a) is simply the value of a.

Slide 3

• Solved Example 1:
  • Consider the matrix A = [5].
  • The determinant of A is |A| or det(A).
  • In this case, |A| = 5.

Slide 4

• Solved Example 2:
  • Consider the matrix B = [3].
  • The determinant of B is |B| or det(B).
  • In this case, |B| = 3.

Slide 5

• Solved Example 3:
  • Consider the matrix C = [-2].
  • The determinant of C is |C| or det(C).
  • In this case, |C| = -2.

Slide 6

• Properties of Determinants for 1×1 matrix:
  • The determinant of a 1×1 matrix is the value of the single element in the matrix.
  • Multiplying the matrix element by a non-zero scalar λ multiplies the determinant by the same scalar.

Slide 7

• Application:
  • Determinants of 1×1 matrices are used in various areas of mathematics, such as calculus, linear algebra, and differential equations.
  • They play an important role in solving systems of linear equations and calculating areas and volumes.

Slide 8

• Key Takeaways:
  • Determinants are mathematical objects defined for square matrices.
  • The determinant of a 1×1 matrix is simply the value of the single element in the matrix.
  • Determinants have various applications in mathematics.

Slide 9

• Recap:
  • Determinants are used to express certain properties and relationships between matrices.
  • The determinant of a 1×1 matrix is just the value of the single element in the matrix.
  • Determinants have wide-ranging applications in mathematics.

Slide 10

• Questions:
  • Calculate the determinant of the following 1×1 matrices:
    • [7]
    • [-4]
    • [0]

Slide 11

• Solved Example 4:
  • Consider the matrix D = [2].
  • The determinant of D is |D| or det(D).
  • In this case, |D| = 2.

Slide 12

• Solved Example 5:
  • Consider the matrix E = [-6].
  • The determinant of E is |E| or det(E).
  • In this case, |E| = -6.

Slide 13

• Solved Example 6:
  • Consider the matrix F = [0].
  • The determinant of F is |F| or det(F).
  • In this case, |F| = 0.

Slide 14

• Solved Example 7:
  • Consider the matrix G = [8].
  • The determinant of G is |G| or det(G).
  • In this case, |G| = 8.

Slide 15

• Solved Example 8:
  • Consider the matrix H = [1].
  • The determinant of H is |H| or det(H).
  • In this case, |H| = 1.

Slide 16

• Solved Example 9:
  • Consider the matrix I = [-3].
  • The determinant of I is |I| or det(I).
  • In this case, |I| = -3.

Slide 17

• Solved Example 10:
  • Consider the matrix J = [9].
  • The determinant of J is |J| or det(J).
  • In this case, |J| = 9.

Slide 18

• Solved Example 11:
  • Consider the matrix K = [-1].
  • The determinant of K is |K| or det(K).
  • In this case, |K| = -1.

Slide 19

• Solved Example 12:
  • Consider the matrix L = [4].
  • The determinant of L is |L| or det(L).
  • In this case, |L| = 4.

Slide 20

• Solved Example 13:
  • Consider the matrix M = [-5].
  • The determinant of M is |M| or det(M).
  • In this case, |M| = -5.

Slide 21

• Solved Example 14:
  • Consider the matrix N = [6].
  • The determinant of N is |N| or det(N).
  • In this case, |N| = 6.

Slide 22

• Solved Example 15:
  • Consider the matrix O = [-2].
  • The determinant of O is |O| or det(O).
  • In this case, |O| = -2.

Slide 23

• Solved Example 16:
  • Consider the matrix P = [0].
  • The determinant of P is |P| or det(P).
  • In this case, |P| = 0.

Slide 24

• Solved Example 17:
  • Consider the matrix Q = [3].
  • The determinant of Q is |Q| or det(Q).
  • In this case, |Q| = 3.

Slide 25

• Solved Example 18:
  • Consider the matrix R = [-7].
  • The determinant of R is |R| or det(R).
  • In this case, |R| = -7.

Slide 26

• Solved Example 19:
  • Consider the matrix S = [1].
  • The determinant of S is |S| or det(S).
  • In this case, |S| = 1.

Slide 27

• Solved Example 20:
  • Consider the matrix T = [9].
  • The determinant of T is |T| or det(T).
  • In this case, |T| = 9.

Slide 28

• Solved Example 21:
  • Consider the matrix U = [-4].
  • The determinant of U is |U| or det(U).
  • In this case, |U| = -4.

Slide 29

• Solved Example 22:
  • Consider the matrix V = [5].
  • The determinant of V is |V| or det(V).
  • In this case, |V| = 5.

Slide 30

• Solved Example 23:
  • Consider the matrix W = [-1].
  • The determinant of W is |W| or det(W).
  • In this case, |W| = -1.