1001 Algebra Problems.PDF

b.Finding xsuch that log 5 1 = xis equivalent to finding xsuch that 5x= 1. We conclude that the solution of this equation is 0. ...

Set 51 (Page 119) b.Using the logarithm rules yields 3ln(xy^2 ) = – 4ln(x^2 y) + ln(xy) = ln(xy^2 )^3 = – ln(x^2 y)^4 + ln(xy) ...

d.The inputs of a logarithm must be positive. Since x^2 + 1 > 0 for any real number x, it fol- lows that its domain is the s ...

b. 5 4 e2–3x+ 1 < 9 4 4 e2–3x< 8 1 e2–3x< 2 ln 1 2 – 3xln 2 –2 + 0 ≤–3x–2 + ln 2 ^23 ≥x> –2 +–3ln 2 2– 3 ln ...

b. 3 ln 4y+ ln A= ln B 3 ln 4y= ln B– ln A ln 4y= ^13 (ln B– ln A) 4 y= e (ln B – ln A) y= ^14 e (ln B– ln A) c. 1 + ln ( ...

a.Two matrices are equal if and only if each pair of corresponding entries is the same. Note that . Therefore, the equation is ...

c. d.Statement ais false because you cannot add a real number to a matrix. As for statement b, simplifying the left side of the ...

c. a.(–2D)(3D) = –6DD = = d.Note that the dimensions of the matrix F are 21. The product FF is not defined because the inner ...

d.The sum G + Ais not defined because Gand Ahave different dimensions. So, this entire computation is not well-defined. d.The p ...

d.Note that (2F)(–2E) = -4FE. Since the inner dimensions ofFand Edo not match, this product is not defined. As such, the entire ...

c.Extract the coefficients from the variable terms on the left sides of the equations to form a 2 2 coefficient matrix. Multi ...

b.First, we rewrite the system by moving all variable terms to the left sides of the equations and all constant terms to the ri ...

d.First, compute the product on the left side to write it as a single matrix: then equate cor- responding entries in the matric ...

Set 57 (Page 134) b.It is known that if is such that det A= ad– bc≠0, then. Applying this formula with A= yields the following ...

d.It is known that if is such that det A= ad– bc≠0, then. Note that the determinant ofA= is zero, so the matrix does not have ...

a.It is known that if is such that det A= ad– bc≠0, then. Applying this formula with A= yields the following: c.It is known t ...

Set 58 (Page 137) a.The solution to the matrix equation , where a, b, c, d, e,and fare real numbers, is given by , provided th ...

b.The solution to the matrix equation , where a, b, c, d, e,and fare real numbers, is given by , provided that the inverse mat ...

d.The solution to the matrix equation , where a, b, c, d, e,and fare real numbers, is given by , provided that the inverse mat ...

the given system can be written as the equivalent matrix equation. The solution is therefore given by. Using the calculation for ...