Section 4.4:4(h) only! 3(a)456(b)7894. Evaluate the determinant of the following matrices by any legitimate.method.-619(124-8125011123(c)12-5(d)-12.5643312(e)(i21-12+i33 1+i2(f) 1-ii1-2i14-iЗі21 0-231-23-12-3112-512--1419(g)(h)0411-922-20312301-49-1415

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Answered: 1-2 3-12 -5 12-14 19 (h) -9 22-20 31 -4…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.5: Determinants

Problem 72E

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Explain how to find the determinant of a 22 matrix.
The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six triple products. Show that the determinant of a 44 matrix involves 24 quadruple products.
FIND THE DETERMINANTS OF THE FOLLOWING 구 1. 3 -9 ー4 5 -8 ー4 3 -8 3 -4 ー7 -3 -2 2 -5 -3 -6 -8
Which 2x2 among the matrices/matrix below satisfy(ies) X^2 -5X + 21 = 0 where I and O are the 2x2 identity and zero matrices respectively? We are given that X satisfy the polynomial x² -Tr(X)x + det(X) where Tr(X) is its trace and its determinant, det(X), is ad-bc when first row is [a b] and second row is [c d]. Consider only the matrices given below: A is the matrix with first and 2nd rows [1 -1] and [-2 4] and B is the matrix with first and 2nd rows [4 -1] and [-2 1]. {SHOW SOLUTION} A = [ ² ] B =[ 1 4 L-2 -2 choices: a) X = A only b) X = B only c) X = A or X = B d) X = A or X = B or X = (1/2)(A+B) e) X = A or X = B or X = (1/2)(A+B) or X = 2(A-B)
Verify the given 7 properties with a suitable matrix (i) If any 2 rows (or columns) of a matrix are identical, the value of the determinant is zero. (ii) If each element of a row (or column) of a matrix is multiplies by a constant k, then value of determinant gets multiplied by k. (iii) If elements of a row (or column) of a matrix can be expressed as sum of 2(or more) terms, then the determinant can be expressed as sum of 2(or more) determinants. (iv) If in a matrix all the elements above(or below) the diagonal is zero, (i.e. if the matrix is upper/lower triangular) then the value of the determinant is the product of the diagonal elements
The expansion of a 3×3 determinant can be remembered by this device. Write a second copy of the first two columns to the right of the matrix, and compute the determinant by multiplying entries on six diagonals. Add the downward diagonal products and subtract the upward products. Use this method to compute the following determinant. со ст со 353 0-5 2 0 5 2 ANO -4 5 0 -5 0 = -4 5 'K a11 12 13 11 12 a21 22 23 21 22 a31 32 33 31 a32
A 3 × 3 matrix M has columns V₁, V2, V3 (in that order). (a) (5) Compute the determinant of the matrix whose columns are 301, 302, 303, in that order. 15+15+10 (b) () Compute the determinant of the matrix whose columns are 50₁-102, 5V2+V3, 5V3, in that order. (c) () Compute the determinant of the matrix whose rows are 50₁ – 102, 5V2 + V3, 5V3, in that order.
Verify the given 7 properties with a suitable matrix (i) Value of the determinant remains unchanged if the rows and columns are interchanged. (ii) If any 2 rows(or columns) are interchanged, sign of the determinant changes. (iii) If all the entries in a row (or column) are zero, then the determinant is zero. (iv) If any 2 rows (or columns) of a matrix are identical, the value of the determinant is zero. (v) If each element of a row (or column) of a matrix is multiplies by a constant k, then value of determinant gets multiplied by k. (vi) If elements of a row (or column) of a matrix can be expressed as sum of 2(or more) terms, then the determinant can be expressed as sum of 2(or more) determinants. (vii) If in a matrix all the elements above(or below) the diagonal is zero, (i.e. if the matrix is upper/lower triangular) then the value of the determinant is the product of the diagonal elements
The expansion of a 3x3 determinant can be remembered by this device. Write a second copy of the first two columns to the right of the matrix, and compute the determinant by multiplying entries on six diagonals. Add the downward diagonal products and subtract the upward products. Use this method to compute the following determinant. Га11 а12 а13] a11 а12 -2 4 a21 a22 a23 a2í a22 0 2 -1 -5 3 2 a31 a32 a33 a31 a32 ..... -2 4 0 2 - 1 -5 3 2 II
(13) BIf (21-A)-! evaluate the matrix A.
1. (a) What (b) What are the seven 2. Consider you have a A matrix as below: 213 A = 1 3 412 12 (b) (40 points) What is the determinant of A matrix, that is to say AA? (a) (30 points) What is the transpose (A') of the matrix?
Evaluate the determinant of 2 1 0 *-17 0-1 2 *-1 - 1 0 Ans= 32

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